----- SOLUTION FOUND -----
Posting a solution here for any CTRL+F heroes

Retroarch Quick Menu > Core Options > HLE BIOS = ON

I don't know what the setting even does, I'm just glad autoload actually works now.
Gonna put some tags below for search engines to pick up on:

lr-flycast, flycast, autoload, auto-load, auto load, crash, savestate, black screen, saves, saving, loading, loads

Update: Installing Retroarch from source seemed to do the trick.