Unfortunately, RP-CRTs are some of the hardest monitors to work on. They're very complicated beasts.
Edge/corner quality on an RP-CRT set is typically only meh at best. Is it fully out of focus (blurry) or is it a convergence problem (red, green, and blue not lining up)? Fixing this may not be worth the hassle.
Honestly, I'd be tempted to rip all the CRT stuff out and drop a DLP or similar in. If you're willing to put up with (or even want) widescreen format, you can probably pick up a plasma with comparable width for a couple hundred bucks, too. These RP-CRT arcade monitors are old and have seen a lot of hours. They're all pretty tired.
As for the conversion device you're looking for, it is commonly called a "transcoder". You need to convert from YPbPr to RGB colorspace and strip the sync off luma. There are devices out there that do this, but I don't know of any fully integrated solutions off the top of my head. Many of them are full digital scalers and introduce lag, but the conversion can be done without doing that.