After some searching and a lot of patience, I finally found a PS1 emulator that uses a similar rerecording system to VBA-rr(GBA) Gens(Genesis/Mega Drive), FCEUX(NES), and Snes9X(Guess).
I'm using version 2.0.2 of PSXjin. If I can keep almost all of the configurations and options the way they are for it, and not run into any glitches or "road blocks" doing this, I should be able to use this to my advantage and finally get a good start on some playlists for PS1 games.
So far, this video's quality on Youtube isn't top notch, but it'll have to do. I like it anyway. This is a great emulator to use for Tool-Assisted Speedruns, as I've seen.
Here's a bit of what I did:
1. First, I start recording internally. I can save and load any movie states from here and it doesn't affect what happens to the gameplay except for fixing any embarrassing or accidental mistakes I made.
2. When that's done, I play the movie I just recorded, and then use it to commence AVI recording. This is external recording, and the videos made from this are viable for Youtube.
3. When that gets finished, it creates a split. The video itself gains an AVI file, while the sounds and music the video had become a WAV file. I use Sony Vegas to put the AVI and WAV files back together, and then render them as one whole video with sound. So far I've only seen this split happen with this emulator and none of the others I've used.
Once that's done, I upload it to Youtube for all to see.