Makes complete sense that lowbar squats felt better for you. I love highbar and front squatting, but I've had a lot of success with lowbar variations with patients rehabbing from patellar tendinits. Mainly because of less knee travel, less anterior (front) load in the knees, smaller knee angle (meaning less compression forces on the patella tendon) and also the load pushed back against the backside. It's a win win really considering what you're saying here, which is also why I asked about the DL. Try to just do a BW deadlifts/RDLs and tell me how it feels.
The reasoning behind your doctor not wanting you bend at the at the waist is likely because the "idea" is to isolate the quads and there's legitimate physiological arguments for this, however, if you're not ready for it it's just not right for you simple as that. Good PT is a cyclical process with continuous evaluation and progression. The version he's doing in the video with the band is not a poor choice, see the idea is completely limiting knee travel here for the reasons I listed earlier, AND, isolating the quads. It's a good enough exercises, and I know the evidence with the isometrics very well, but it's still not my favourite personally. It can work well, but if you get pain as you say, I'd much rather opt for a sitback quarter squat with forward lean and hips back (lowbar) or various deadlift variations, as they offer many of the same protections with the additional benefit of letting you engage your hips, glutes and hamstring much more, which in turn can help you in the long run.
Are you doing any soft tissue work (stretching, massaging, breathing excercises)?