Hey man, love your attitude, and you're right about the quads as well, great assessment.
We can change your squat, and we can do it quick, i'm writing another article for T-Nation that deals with this problem, and how to re teach yourself how to squat, I should be submitting it monday.
Anyhew, here's what's going on:
1- you have long legs and a short torso
this sucks because the bar has to stay in line with the center of the foot or you're going to miss the lift... unless it's light. Because your legs are so long, and your torso is so short, you need to lean very far forward to keep the bar in the right place.
I'm sure this sounds frustrating and you already knew, but here is where we get to the fixes
2- Bigger heels
you're wearing the lower level version of the adiddas with the .6 inch of a heel, as soon as possible get shoes with .75inch of a heel, or get heel lifts for your other shoes. I gave a friend of mine Do Win weightlifting shoes that have a 1 inch heel, maybe more, and his squat changed right away. The heels allow your knees to travel further forward, so you butt doesn't go as far back, making it easier to line the bar up with the center of the foot.
3- No more low bar
I hear all the time about low bar powerlifting... it's good for some, but not for you. Once again, a lower bar position is going to force you to bend over. Everyone says you squat more, cuz of the whole posterior chain, but keep in mind that advice is coming from geared lifters with knee wraps and suits that aid in knee extension out of the hole... because of this, quads aren't a big deal in training today because all the articles say you don't need them... and maybe that's true for gear... I dunno, haven't worn it in a while but for raw? no, you need quads big time, especially with how deep you squat. Low bar actually takes the quads out of the lift, and getting out of the hole below parallel is hard without strong quads.
4- ditch BS for 6 weeks and just FS
Google russian squat routine. When I rebuilt my squat I did the 6 week program and hit a nice PR, then went back to BS and my form dialed in. This will be extremely beneficial to you... I'm really serious here... I can already feel you getting antsy, so just remember, you want to UNLEARN your current form, you want your BS to feel unnatural, so when you go back to it you wont be tempted to go back to your old form.
5- when you go back to BS do not do reps
Nothing over 3 for the first few months, every rep counts and every rep has to be as perfect as you can make it. When you go for reps, form is going to break down and you'll just teach yourself to squat the old way sooner or later. I hear how form is never going to be perfect... but none of those people are olympic weightlifters or the powerlifters I know. Start at 70% for 3's of your old max, and work it up slow and if form ever breaks down lower the weight or stop. I'm sure you know all of this of course, but ti's worth saying.
6- Don't take my advice to heart
It's gotta be your hand on the wheel man, unless you have a regular consistent coach, you're on your own. When you're a ronin like me, everyone has an opinion and is an expert... everyone. You have to be your own expert man.
I liked your squats, I think you're going to look amazing when you get this figured out.