Tried again this morning and immediately got a better run. Shaved 6 seconds off. A few places I could've played a bit better, but no major mistakes like last time. If I clean it up I can get sub 5. Better RNG or routing changes could bring it lower.
And... I improved on the last run almost immediately. Still has plenty of room for improvement (that first jump is kind of embarrassing and the last room is ugly.) I think if this were cleaner it could be around a 3:15. If I could find a way to get through the spikes without the float then we could get really low.