Also, I've defeated your creation via integer overflow :D

Excellent prototype. I did notice a few issues during my playtime:
- Coin doesn't work. Console error is showing "Error: Invalid item id: Coin" from file core/variant/variant_utility.cpp:1023. No cash is earned when scored.
- Softlock in the shop happens infrequently but at-random, where the proceed button no longer works. Might have something to do with rerolls.
Very inspired design overall, taking inspiration from existing score-like games but with a fun, distilled twist on it. Would love an .exe version with save slots!
From my own experience (made a game in the same genre), players cared a lot more about a smooth/lag-free gameplay experience than about visual effects or tactile-feedback, especially if they're in the end-game where numbers get huge. There are some things you can do to optimize without a hard-cap; sprite-batching is a big one.
In the end though, a cap is the most practical. One simple technique you could try is to pool the 1,000 visible-entities separately, so your actions can bind to one of them randomly and always produce a visual effect. A subtle tradeoff that still provides that visual juice! :)
Now THIS is insane for 4 hours of dev time. I think your implementation of these little roguelike elements is excellent. Would be nice to have a little indicator on your box that reminds you with direction (horizontally) you're currently moving in. Actually, when you hover a dice, you could get a "ghost" indicator that tells you where you'll end up if you use that die.
Getting a bunch of chests can quickly allow you to go infinite, but I am seriously impressed with this.