Leaderboard as of today (I think) Carlmanger - 1:24:00 - Lightmopp - 1:37:25 - Zinpars - 1:37:44 - 613Spiral - 1:49:17 - Hydrofire593 - 2:00:51 -
Other relevant videos Carlmanger - 1:17:27 with 1 jump - GameChamp3k - approx 6:25:26 but not a speedrun -
With Spiral's new PB that respects the rules, that makes 5!
My guess is that, like any new unofficial category, it is not safe to assume the ruleset is definitive. It will crystallize as runners improve on the route. The good news is that those rules don't really matter much for now.
I think the switch to 2P can be allowed under two simple conditions: the switch to 2P has to be made between the first and second cutscenes after the final Bowser fight, and no movement input on the 2P must be made after Mario has awakened after the second cutscene, forcing the switch back to 1P.
Also, the second rule (the 5 min penalty) was somehow arbitrarily created because for some, there was no way or knowing if the ground pound glitch to talk to NPC worked, but it turns out there is a way to tell by analyzing some patterns in the particle effects. It also helps by not having to reset the run if you jump by reflex. Though anyway, this rule won't matter for the top of the leaderboard.
Also, ending the timer at the same place as any%, versus on the Toadette 0-jump screen will depend on if we consider this category to be "any% but with the constraint of no jumping" or "fastest way to see the 0-jump screen". I personally prefer the latter since that was the reason Gamechamp3k made the original VGmyths video that this category was inspired from, but the former is more related to other runs - and also will have lower time.
The more people run this and optimize the run, the clearer the rules are gonna be.
1:37:25. You can use this route as well.