So I just finished a Krastorio 2 game where Even Distribution worked as intended - ores, intermediate products, and tech cards were distributed automatically to labs, machines (and boxes, which...why?) nearby when using the cleanup key.

I started a new one with Space Exploration (and AAI Industry, because that's needed for SE to work) added and while it works with products like Copper Wire, it no longer works with tech cards, coal, wood, or ore. The click and drag still works, but Inventory Cleanup was such an absolute lifesaver in my previous game that I'm not sure how I'm going to cope without it.

Is there a setting that needs to be changed so that it will once again simplify my life by stuffing the labs and assemblers with the things they need?

Yes, there is no default configuration for Space Exploration yet. You can create personal logistic requests (or autotrash) for all the items manually and it will distribute everyhing above that amount.

I ended up adding the sciences and ores, and bringing the plate count way down so it would actually empty the inventory, and now it seems to work fine (although it seems to like keeping hold of stone sometimes).

It's kind of weird that it was perfectly happy to get rid of tech cards in Krastorio, but once I added SE it didn't want to know, but I got it sorted :D