@jlmoss: what Hoose said, stay upright as you go down. Significant butt-wink at the bottom too. (where you tuck your pelvis underneath you). Lumbar flexion under load... been discussed ad-nauseum on this board.
Disclaimer: I have the exact same problem! So... if you figure out how to fix it, let me know.
Not that I'm suggesting that lumbar flexion is a good thing*, but it's really end-range lumbar flexion that's necessarily problematic and injurious. Stuart McGill talks about this in some detail when he was studying the spines of powerlifters, most of whom ultimately lift with some degree of flexion in their spines. Injury occurs when the spine is flexed fully
, partial flexion, skillfully employed, avoids injury. End range flexion with just the weight of your torso and insufficient muscle support will injure you far more assuredly than partial flexion supported skillfully by powerful trunk musculature, which is why people will throw out their backs picking up a pencil.
I don't fully understand the science of it, but it seems that back extensors at the right angles are able to successfully compensate for additional shear forces caused by small amounts of spinal flexion. Unless you lean forward and change those angles, which is why I bring it up. Take a look at an olympic lifters ATG snatch or front squat. You might see some spinal flexion, but what you won't see is any significant forward lean.
In terms of how to fix it, hammer the heck out of your hamstrings and especially your glutes. Tight hip flexors and a weak posterior chain not only make it difficult for your body to get into a proper biomechanical squat, they also ensure you lift with your quads and not your more powerful glutes. Do some mobility work for those tight hip flexors, and do some rock bottom front squats and slightly-wider-than-normal deep back squats. Throw some sumo deadlifts in there too.
Specifically at jlmoss: I think I see some external rotation happening with your feet there (can't tell for sure from the camera angle). If that sounds familiar, roll your piriformis on a tennis ball stat, and do a lot of glute activation before you get under that bar.
Dictated but not read.__________
*seriously though don't perform squats with lumbar flexion with any kind of serious load unless you are a competitive lifter. Why take an unnecessary risk?