Huge thanks to @108Pi for helping me encode this TAS in Mesen-S, because I couldn't find a way to play the movie until he helped give me a script that could convert bk2 files to msm files.
@Niftski Wen upload TAS

Framecount: 70956 (19:40.656 TAS Timing)
Rerecords: 24944
BK2 File: https://drive.google.com/file/d/1PGN-3FuoTYGV9SevUJheLSliGAKNaXZR/

Notes:
I had to delay a framerule on the title screen to avoid bad bars in 5-4. That was unfortunate, but what else is there to do?

2-4: Got a kind of bad bar, but not enough to lose the framerule.
5-4: I still did get some bad bars even with delaying a framerule, but this also wasn't enough to make me lose a framerule.
6-2: Something weird happened here when I tried to play my TAS in Mesen-S. There was an extra lag frame during the transition from 6-1 to 6-2 for some reason, desyncing the entire TAS after that. It was kind of annoying to fix, especially since I wanted to try to see if I could remove that lag frame (which I failed to do). This means the BK2 file I've shared only works on Bizhawk, and not on Mesen-S.
8-3: Normally with Fire Mario you can't get backwards pole, but if you gain enough xpos (you need at least 150), it is actually possible. It doesn't actually save any time, because it takes too long to gain that xpos, but I did it for entertainment purposes.
8-4: With Fire Mario, you can still do walljump room as fast as you can in normal SMB1 (and the other rooms, of course). It's a lot tighter since you're required to do a 2 frame jump for the walljump.
For some reason water room is really prone to lag, so I was only able to reduce it to 3 frames of lag. Shoutouts to @Simplistic6502 for helping me understand more about lag in water room.