Man, video footage. That’s awesome!
Judging from that video, the biggest thing you might be missing is a keen sense of when you hit hamstring end-range tension at the bottom of the squat. Getting the hamstrings lit up is one of the major benefits of leading with the hips back, and being able to stay connected to that tension throughout the movement is important for staying tight and stable when you hit the bottom.
It’s hard to see with the rack in the way, but it does seem like you’ve got a little change in pelvic position happening at the bottom of the squat (the dreaded “butt wink”). The older video of you squatting 135# shows it more clearly, though old footage is old footage. What this shows is that you are trying to get lower in that squat than either your motor control or mobility (or both) allow.
Now here’s the thing. Loaded squats with clean technique will do wonders to drive your bottom position deeper and open up the hips and hamstrings. It’s almost like magic, when you try a few air squats before and after your heavy sets. However, if you are unable to sense where that true bottom position is (or you are very eager to have a deeper squat), you’ll never nail the same kind of end range tension and be able to reap that awesome benefit.
Here’s what I would strongly recommend for your loaded squat practice (assuming you’re not already doing it): slow eccentric reps, paying very close attention to how deep you can go without faulting (keep your hamstrings on tension); and pause squats (start adding a 2-4 second hold in that good bottom position). These things will necessitate a bit less weight, but that will probably only do you good.
Also, something’s making think you’re losing stability coming out of the top position, and this may be related to how loose your arms are on the bar. You need to hug that thing tight to your back.
Also, also, if you could get some footage from the front/back, both at full speed and slow-mo like the one you posted, that would probably offer even more insight.