Yeah I'm with Jigglyball here. Because you need to bring the bubble from level 8 into the room after it, this strat would probably be slower than just going down to get the bubble and riding the stream up.
I just went ahead and tested the coolmathgames version, and it seems to be identical to the itch/steam version in terms of timing. As long as you make sure the timer is visible in the top right corner and adhere to the other general rules, then yeah, I'd say you're good to submit them! I'll make sure to change the rules to reflect this!
Yeah, getting on the wall has been extremely finnicky for me in the past. You have to be as close as possible to the top of the left wall when you do your wall jump, and you have to make sure to hold away from the wall before wall jumping, since that gives the most height (for some reason there seem to be two different types of wall jumping: one that gives more horizontal speed and one that gives more vertical height. For the vertical height one, you have to hold away from the wall right before jumping. It will make a different sound than if you jump while holding towards the wall. If this is unclear, I can make a quick video demonstration).
As for where I figured it out, I found it on my own. I theorized that it was possible to get up there and then make that tricky wall jump up to the O2 tank, and that it would be slightly faster than doing it normal way, so I grinded it out until I did it. It is far more useful in All Gems though, so it is definitely worth learning if you're thinking of perfecting the level.
Yeah, I do this jump in my Any% Chapter 1 WR, and it is definitely a tough one. The key is after getting onto that wall you got to, to fast falI and jump as late as possible over to the other side. It's very tricky, so I can go through and make a more detailed tutorial later if that would help.