I have been playing Tetris non-stop for about a year and a half and only recently wanted to try speedrunning... problem is, I can't record myself doing the runs unless the game has a built-in replay system (Jstris and NullpoMino so far) which limits my options to play

Welcome! Have you thought about recording with your phone if you have one with a camera? Most communities allow it as long as the quality is decent. Good luck on your runs.