I made some changes/updates to the Any% route which can be seen here.

The main change is instead of doing "The Game (45)" quest you collect 5 Silver Keys (for two 5 Key Chests that contain 10 Guild Seals each), "The Final Insult (5)" quest, "Restoration (5)", and 15 Guild Seals from interacting with people.

Sub 3:50 should be possible I think.

I posted a link to your route in the Any% guide. I probably won't come near this game again with a 10 foot pole, but your discoveries may make me have one more go at it.

I think my estimate was pretty far off on the route change. I had ~4:30 to save just from not sitting around waiting for day to buy food for the demon door. I ended up saving ~12:30, which means I saved around 8 minutes from the change. I don't think there was anything I really did in my first attempt that would have made me lose 4+ minutes otherwise.

Also I have no idea what happened but when leaving Bowerstone Industrial on the boat to go to aurora the load took an extra ~44s compared to my first run where it was pretty much instant. I thought the game crashed and was pretty close to just turning off right before the cutscene finally loaded.