As promised.
Cascade needs so much support that it does end up warping a lot of other choices. I doubled up on a couple cards, and I'm trying out some Exile-matters stuff alongside all the Foretell/Adventure/Cascade/etc. that naturally exiles, in addition to Protocol/Drift. We'll see if that's too cute, or if that starts turning it into the "cascade" cube too much.
Still plenty to test out.

Been a while.
There's been a bunch of relevant stuff printed, so I'm doing a massive update/reset. This is an incomplete update because once I make changes I want to get a feel for what's missing (not to mention the Drift cards that aren't in the database yet). I'm also updating the philosophy to just be more all-in on the components related to Cycling or directly related to the cards it demands (e.g. Wx enchantments is still likely to stay given how many enable cycling benefits), and to not worry about making sure each color pair has a perfect theme, or to avoid duplicates... so long as there's some interaction between its cards, and the iconic decks are draftable.

There's not much of a critical mass of enchantments otherwise. Skyturtle is also just great.

...and including some experiments like Summer Bloom.

Still getting to a baseline to reevaluate and add in what's missing (mostly glue & answers)...

A lot of exciting MH2 cards (more cascade and suspend); we'll see if it works!
I'm minimizing the doubles again; I still think 1 in each color is... OK. I'd still like to find replacements for the doubled single-color lands (Barren Moore, etc.).
Especially with the new priest, WB just makes more sense as reanimator. To some degree this means black is just the "graveyard recursion" color (BU Mill, BG Spawning, BR Cast), but maybe that's OK.
Adding more mill to blue; they're not designed as engines, but more as gotcha's against the greedy control decks that otherwise have the board locked. Peregrine Drake (alongside Cloud of Faeries) should hopefully make Escape Protocol a lot more interesting.

As I draft with bots, I keep reaching a point of "Oh... well now that I have these ~3-6 payoffs, I just take all the good cycling cards and I'm set, right?" This also often means falling into Jeskai, where most of the best obvious payoffs are. This is fun when it's rare, but not when it's every draft; it's also not interesting gameplay to just cycle to your payoffs then win or lose, glass-cannon style.
Removing Irencrag is step 1, but I think I need to take a harder look at some of the other "easy" payoffs. Astral Drift, for instance, is a great card but its engine at least requires specific drafting & deckbuilding skills. Hopefully aggro decks can get underneath them or can remove the key payoffs easily enough that "take all the cyclers" becomes not always correct, but that's hard to test without playing out the games.

Not all cyclers or payoffs are created equal, so I doubled up on some cards that were especially good in certain archetypes or styles of cycling decks (Fox for Boros, etc.), or helped generate a critical mass of other effects.
I'm trying out the new WR theme in Strixhaven ("leaves graveyard" triggers) since that lines up nicely with BR, and several other effects. The "leaves" triggers don't seem that strong, but hopefully still aggressive enough to be decent.
I also realized that A) GW Lands was pretty far off from the rest of the cycling stuff going on that I didn't need to push it so hard, and B) In addition to shifting away from the themes of my original cube, I also need to shift my mindset off of "this color pair needs to do this specific thing, because that will help newer drafters" to "what cool sets of cards work well together and can preferably also work in various decks?" The latter will take me time, but it's a start... this cube is very much still in the brainstorming phase...

I once again forgot that Stone Haven Pilgrim is not on MTGO apparently. Oops.

I'm too married to my original cube. This cube is its own thing.
Time to reevaluate it holistically again...

...From the top...

What do people expect from a cycling cube? The most well-known tournament-level iteration is probably Living End, so a cascade/suspend package to live that dream seems great. Next is absolutely Astral Slide/Drift, so that's in alongside as many other good build-around enchantments/there are that specifically call out cycling.

From there, what are the components of cycling we can leverage?
Draw triggers. --> Faeire Vandal, Jolrael, Irencrag Pyromancer...
Discard triggers. --> Brallin, Bag of Holding, Bone Miser...
Creatures in the graveyard. --> Spider Spawning, Reanimator...
Non-creatures in the graveyard. --> Delirium? Spell mastery?

So after adding a lot of those cards, here's where the identities stand...
RG - Cascade; with minor trample, 3+ power, and "lands in GY" themes
BG - Spiderspawning and recursion
GU - Cascade & draw triggers
UR - Looting / Spells

(Notably, 3/4 green pairs are listed, but none in white.)
Which brings me to emergent strategies based on a lot of the cards "locked" in that color:

WU - Enchantments / Historic
There are a lot of cycling payoffs in these colors that are enchantments, plus Ardent Plea matters more in this context, so it seems sensible to build around enchantments. That's not really enough, so taking inspiration from Glassdust Hulk, "Historic" captures as much overlap as we can here. Of note, there's also a minor blink theme in WU with Astral Slide and Escape Protocol, so keep an eye out for cards that play into that.

WG - Might as well finish the last green pair. There are a lot of options here (+1/+1 counters & enchantments tying for 2nd, but there's also tokens, threshold, hatebears...), but to manage the balance of white's odd split between aggression and control, and green's giant creatures with cycling, I'm going with some aggressive ramp. This supplies it with card advantage, let's it capitalize on the karoos better than the other colors, all while applying pressure. In theory anyway. We'll see how it goes.

BR - This one's less clear, but since there's a reasonable amount of discard triggers in red (and so also some flashback), and black wants stuff in the graveyard for spider spawning anyway, I'm going to start by trying to make this the Burning Vengeance deck. Chainer, Gravecrawler, Squee, Dreadhorde Arcanist, and retrace help to suppliment Flashback and Aftermath effects. Madness was another option, but just didn't seem strong enough (too much of A+B). Sacrifice seems OK, but pretty disconnected from what all the other themes.

So to recap...

WU - Enchantments/Historic
UB - ??
BR - Vengeance
RG - Cascade Aggro
GW - Lands
WB - ??
BG - Spawning / Reanimator
GU - Cascade Value
UR - Looting
RW - ??

UB Self Mill:
Though still missing a WB theme, Black so far really wants stuff in the graveyard. Blue so far is also great at drawing a lot of cards. Combined, a UB self-mill theme seems like a snug fit.

WB Blink:
White has a lot of blink potential in its two themes so far (landfall, sagas); black has the unearth ability, which both plays into its BG, BR, and BU themes, but is a very sneaky way to abuse those blink effects and keep your creature forever. It can also reuse ETB effects just by bringing creatures back from the graveyard.

And then there was Boros...
RW+ Cycling was a fun Ikoria Standard deck, but a miserable draft deck. The biggest offender was certainly Zenith Flare, and while it might be an appropriate power level here (maybe not) I'm OK never seeing that card again in draft.
That said, there's not much other overlap between the two: red wants to discard aggressive flashback spells; White wants to play aggressive historic ETB/landfall cards. Boros will take some experimenting, but for now I'm just leaning into its aggressive side with some combo potential: Zirda & Feather. Zirda is obviously great with cycling, and Feather is pretty good with the blink instants in W and a few spells in R. We'll see where this goes.

So...
WU - Enchantments/Historic
UB - Self-Mill
BR - Vengeance
RG - Cascade Aggro
GW - Lands
WB - Blink
BG - Spawning / Reanimator
GU - Cascade Value
UR - Looting
RW - Zirds of a Feather

And this is our new baseline. There's enough complexity to allow plenty of other decks than just these 10, but beyond the primary pillar of "good with cycling", this at least provides some secondary pillars of cohesiveness to center future changes. Because it's such a huge overhaul, it's still going to need quite a bit of analysis before settling, but it's at least a better starting point than a completely different cube.

Making some adjustments for things I didn't realize weren't available on MTGO, as well as some cards that are a bit too expensive to justify spending on this (namely Shark Typhoon and Wanderer, which together were 25% of the entire cost of the cube; I could see adding them back in later).
While we're at it, a couple more obvious swaps I forgot about before.

Now that I can see the whole list more easily, I can replace things that look bizarre, or out of place, or under-powered. Still a lot of adjustments to go, I'm sure, but this gets it a lot closer (I hope).

Things I'm watching:

• I might be wrongfully hanging onto Famished Paladin combos to supplement the ones with Traxos (which I could also be wrongfully hanging ont0); maybe I can look for other infinite combos that are more integral to the drawing/discard/ETB nature of the cube (such as the last minute Kitchen Finks addition).
• Am I hanging onto Zombies too much?
• Is Cascade too strong? Do the suspend-decks even work with it?
• There are several other cards "on-watch" (like Witch's Oven) that I'm happy to replace, but want a better feel for the texture of the cube first...

Replaced a ton of stuff (somewhat at random) to add in all the cool ideas now that nothing is off limits. Taking a breather now, and figuring out what it looks like, what's actually supported or not (is there still a minor artifact theme worth supporting? Infinite combos? sacrifice? equipment? etc.) and what looks fun that I can push...