I know they are tied to my save file somehow because I tried starting a new file to test the issue and lo and behold, Link rolls normally and floats with cuccos.
I've tried using a new iSO, so I know it's not that. These issues persist whether I load my game via savestate or the actual save system. I'm at the Falbi's Flight by Fowl platform and Link just drops straight into the lake holding the cucco every time.