Well, try a bodyweight assessment. I've used this to tire the shit out of some very raw beginners, but it also helps connect mind/muscle....
Use the squat cage and have him grab the uprights to balance himself. Focus him on a) chest pointed at the ceiling (not pointing outwards, but UP) b) back shoulder blades scrunched together tight, c) the big one: tell him to try to touch his shoulder blades to his ass, and not leave that position.
Then have him walk himself down with his hands on the upright to balance, finding the spots that are difficult as he goes down and correcting. Get him to sit in the bottom squat position and force everything tight. This should be easier because he doesn't need core stability with his hands pulling on the uprights to balance himself.
He probably has trouble "internalizing" what it means to try to touch his shoulder blades to his ass. So, have him do sets of "supermans" on the floor for sets of 6-10 reps between the upright form testing. Hold each rep for about 5 seconds. He's going to cramp like a mother, but he will definitely feel his low back contract. Tell him that cramping feeling is what you want him to feel at all times when squatting, then have him use the uprights again. I have absolutely made raw novices sore as hell just using this as their only "squat" work. After a little while, they start to understand what you want, and because they can feel what is happening in their muscles now it is easier to replicate.
When you get tissue quality issues sorted with the foam rolling you're doing, this is going to make it a lot easier for him to move.
The other things I would suggest are db or kettlebell swings for hamstrings and glutes, and goodmornings/back extensions for low back--obviously with extremely light weight to focus on form and repetition. For guys it's often hard to "feel" what is supposed to happen, which is of course a major problem that compounds already existing motor pattern problems! Hard to say without watching him squat, but it sounds like in addition to motor pattern problems he just has a really fucking weak low back and hamstrings. If there's no strength to tap, there's no strength to stabilize a squat pattern, no matter how light.
You can't recruit a muscle that you can't feel effectively...
Anyway, I'm sure you already know and do this so I am preaching to the choir by suggesting this, but I would say hammer ab work (specifically anti-flexion or anti-rotation work) and hamstring/glute/low back work with appropriate isolation exercises, working on gradually integrating slightly more complex exercises until you can get him to start squatting with a posterior chain he can feel working. I would say do a set of ab work in between every damn set of every day you train together. Well, at least for the first exercise or two of every day. frequent work needs to happen for this guy.