This is probably the best I'm going to be able to do. If I grind out the first menu I could probably get faster at it, but the amount of blessed RNG from getting quick shop parts, to running only 4 floors in Sunken Ship and skipping floors 4 and 7 for Sun and Moon avoiding two cutscene triggers.

I thought 2.30 was pushing it as far as the route limitations, but I think this could go even below 2.20. We'll see.

Edit: Video link was broken and did not show the whole run. Should be fixed now.