am I allowed to submit a run recorded on my phone? As of now, I don't have any video capture hardware, and I'm recording my run on a PS2. The quality isn't unbearably bad.

Yes, about every speedrunning leaderboard known to mankind allows bad quality, if you can at least make out shapes. Most leaderboards understand that not everybody wants to spend money on a capture card, or doesn't have one.

Though, in the future, I would suggest using Discord, if you haven't already. Runners of the game are pretty responsive:

https://discord.gg/83A6Pts

Well I ended up getting one anyways. And I joined the discord already