Badge tutorial skip is useless
So as for use of Badge Tutorial Skip in TAS, it looked promising because we aren't buying anything in Beantown in the anticipated route anyway. But since Mario doesn't have Bean Badge equipped, the Popple fight takes 1 round longer which means Rookie enters his fire-breathing cutscene which ended up burning pretty much all of the time save.
-30 seconds estimated time save (Badge Tutorial skip)
+26.5 seconds lost (longer Popple fight)
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3.5 seconds save
I don't think we can bypass the trigger upwards (to enter the castle after triggering the endgame) and then downwards once more (to go on our way towards Mountain Village) in less than 3.5 seconds. So it seems useless to me.
You can bypass the trigger in 2.8 seconds and come out with a timesave of 0.7 seconds. But you miss out on bean badge worth 14 coins later and you cannot get those coins elsewhere in 0.7 seconds or less. So, useless trick.
Jump course skip is useful
As for the jump course skip, I was skeptical if it saves time since it misses out on 1 Syrup and 1 Mush.
So I looked into it; with the current route, the Stardust "2x Fly, 2x Cannon" fights would stay the same except I do 1 fewer Splash Bros. I can't insert extra Splash Bros anywhere except in Hohooros. That would solve the "1 less Syrup" problem and I don't need to collect an extra Syrup, but Hohooros takes longer.
-14.66 seconds saved (jump course skip)
+11.6 seconds lost (longer Hohooros)
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3 seconds save
We lack 1 Mush but it should be possible to get one within 3 seconds. The current route gets +2 Mush in one "2 Fly, 2 Cannon" fight and it should be possible to get +3 within 3 seconds of RNG manipulation.
There is 1 Mush in sewers I could get that takes 55 frames detour, so depending how RNG complies in Stardust, I decide between
- two +3 drops, one +2 drop (Stardust) & 1 Mush from sewers
- three +3 drops (Stardust)
Depending what route RTA does, it might not be a timesaver in RTA. Assuming it only saves 3 seconds there too and you spend 1 second to lign up the bros, you'd only save 2 seconds if you get it first try and waste time if you don't.
