My best is 5:14, I just reached a point where I can consistently cap on every boss but my murgoth's soul only does around 30m still. With a lot of funding soul weapons can really shave off time since their damage isn't capped and they have a much larger range than QT. I know I've seen a few people with murgoths that do upwards of 100mil damage, which can 1hko the first 15 or 20 floors of dojo, meaning you can run them like a phantom would (waiting on the portal and entering as soon as the boss spawns/dies).
wasn't fully funded but i had never done dojo and i had just reached 600k range. quit right after because i realized i still needed to complete and cube the gollux set and make a whole new RA set qq
and oh my god cannot get myself started on upotting + cubing the dumb emblem