Ken,
Great question.
There are a finite list of chord sequences in standards that will get you to 99% of what you will encounter. the ii-V-I being the most common. When you analyze a tune and define the basic structure, you can create a chord melody by using the basic chords as written on the fake sheet. As you develop more as an improviser and digest more substitutions and add extensions and alterations to your chords, you become more sophisticated. JP is on the Mount Rushmore of solo jazz guitar. As you move through the material that Barry presents, you can see that through years of practice he can see a melody note on one of the high strings and quickly recognize the harmony beneath the melody which will either create a two note diad or a chord of some sort.
The best way to evolve into that style is to make sure you invest as much time in the chords as you do the lines. There is a Joe pass book that many swear by that may also add some insight into his substitutions in his solo pieces.
I saw Joe in the early 90's in a small club here in Austin and he plugged his Ibanez directly into a Polytone and basically just played for two hours straight making his setlist and everything else up as he went along. A true Virtuoso (pun intended). That is what I have always aspired to. I can't sing, so to able to pull out a guitar and entertain with nothing to accompany me would be the biggest reward of my many decades of dedication to the instrument.