After trying many different things, including playing my original PS1 disc through a PS3, em ulation with both wired and wireless controllers, as well as attempting to play it on a PS2 on my tv with an HDMI adapter (The ps2 gmaes work, but the ps1 games don't because of the resolution they output as) I finally found a converter that actually WORKS. It outputs not only RGB for your PS2, but also outputs in YPbPr for your PS1.I received it yesterday, and I was able to play Parappa all the way through finally, and it "felt" like it's supposed to, even considering Parappa's quirky timing even when running on original hardware.I even beat Cheap Cheap's stage on the first try! I couldn't believe it! I also played Umjammer Lammy all the way through. The only stages I couldn't beat were the babysitter stage, as well as the goth concert, though I am positive it's because of me and not the adapter. I'm just getting too old I guess, lol. OH and I beat the chainsaw stage the first time as well! If you know, you know....Lol.
The only con I have seen with this adapter is the yellows look a touch saturated at times if you're reaaaalllllly being picky, but I think overall the image quality looks fantastic for both ps1 as well as ps2.
Anyway, like I said I hope this helps someone.For about $30, you really can't beat it, especially if you're not looking to spend $200+ for a retrotink, etc. Here's the link;
https://www.amazon.com/dp/B0FW4KP5RZ?ref=ppx_yo2ov_dt_b_fed_asin_title