After sleeping on it, the answer became obvious. If you need to do anything Magic-related in multiples of five, there's only one option: one of each color.
270! Now each Winston sees 1/3 of the pool, which should offer up approximately 20 lands in each pile.
Also, selfishly, now I only need 300 sleeves. I won't claim that was the primary force driving the slim-down, but it was definitely a factor.
Wanted to get down to 270. Currently at 275, and those last 5 are not forthcoming. Might need a second set of eyes on this.
How many variants of Shimmering Grotto could there possibly be? Well, there are currently four I don't have here (ignoring a few Commander-specific ones); I'll hunt them down when I feel like it. But I think I have the rest...
For now, I continue to fine-tune the colored mana gimmick here. Gone is every land with a repeated two-color activation, as are a few of the lesser color-requiring cards.
90 cards is a hard target to hit. Hopefully this gets a few more lands into the mix.
Since I wanted to use this cube mostly in a Winston environment, 360 cards was simply too large. Most Winston pools are only 90 cards, or 25% of 360. Stripping down to 300 cards brings that percentage to 30% while also concentrating the overall pool to make synergies more likely.
After watching LSV Winston Draft a mono-red cube, I was inspired to make a Winston Cube of my own. Since my primary cube is all multicolored, it felt right that this one be entirely colorless. Since the only available basics are Wastes, all colored sources must be drafted — and those sources aren't being provided without a price of some sort.
The hardest part of building this was finding enough "white" cards to balance the other colors. For a while there I was considering 11 white vs 21 of the other four, but I did some research and found another 10 that weren't awful (mostly thanks to a couple of recent Commander decks). The "multicolored" cards aren't evenly distributed, as those numbers simply don't exist — again, largely because white doesn't overlap with devoid very often. I'm also not counting lands as part of their respective color identities; there are just a flat 60 lands in the cube, and whatever colors they ask for is irrelevant.
I don't think I'm going to update this very often, but now it's done (minus a few singles... and 400 sleeves... I need to pick up for my physical copy) and available. Have fun!