I was thinking leaky injector at first but you said ALL of the spark plugs were wet, right? I don't know how all of them would be leaking to that extent. When you pulled the fuel rail to install the fuel pressure regulator, did you mess with anything else on the fuel rail?
To answer your last question about the code 35 (though I don't think that's going to cause the issue, if it's bad may as well address it while you're fixing things.)
Courtesy of the
Factory Service Manual
I'd start checking off common problem areas. These things could be causing your rich issue without throwing a code. Or you could have a combination of issues.
https://www.youtube.com/watch?v=V-Mwxicmpg4
DIY video on checking/adjusting your TPS.

FSM on testing your knock sensor. This would likely throw a code and while it puts your engine into limp mode, it shouldn't make it run so rich it won't idle.
I'm not normally an advocate of throwing parts at something but I'll make an exception for the Coolant Temperature Sensor in this case. It's kind of a pain in the butt to test and at that point, you've already removed it from the system. A bad CTS may not throw a code but it is an input to the VE tables and warmup tables for the engine. If your ECU thinks it's really cold it'll give it more fuel on startup. Don't confuse this with the gauge on your dash; these cars use 2 separate sensors for that. Make sure you get one like the one pictured. Should be able to pick it up from your local parts store for less than $20
MAF
If you do this, be VERY careful not to short out the wiring while taking a measurement and make triple sure your multimeter is set to read DC voltage before you connect it here
If you want to do a quick-and-dirty on the MAF to tell if it's bad, you can backprobe between the solid black and solid white wires on your MAF plug (pins C and D on the last page here) and you SHOULD be reading 0.8-1.2VDC
The catch here is that's voltage with the car idling and MAF plugged in. Backprobing is connecting to the wire harness side with it still installed in the system. Be careful not to damage the pigtail here. Easier method would be to borrow and swap out MAFs with a buddy who has a known good MAF. If you don't have one and/or want to spend the money to shotgun it.... well here you go.
