It looks like the J122 should do it. You have a trimmer R39 that should help. Matching them would give the best chance of a good phase effect.
Socket the IC's!
Thing with the LM324 is, it was designed to work all the way to ground, which is good for many non-audio path jobs. Most op-amp outputs swing within about a volt of either supply, but the 324 can swing almost exactly to ground, however, it pays for this by not being able to swing very close to the + supply. Expect within about 1.5v of the + supply voltage. This doesn't mean that it can't be used in the audio path - it can and often is, but the asymmetric output swing has to be considered. The phase shift amps have 6volts bias, so this is close to clipping at the positive swing.
The first amp the signal gets to actually reduces the guitar signal by almost a 1/3rd (100k/270k), so this design doesn't want a big signal at all (9volt JFET phasers are notorious for distortion with strong signals), so I'd expect the LM324 would still be ok for headroom except with a run down battery, and you'll probably use an external 9volt feed anyway.
"If I get one working I would happily send it down to Wales so you can do a scope trace!"
Sure, if it has a passport
