A couple of things that might help you.
"When my feet are off, that means my legs will also be out of alignment, which I can also feel throughout my back being not straight, which effects my shoulders......"

Well, at least you are noticing these things. Isn't funny (well, maybe not funny)that if one part of the structure is out the entire structure is out.

"...but it feels like a bigger problem than you guys make it out to be. In my weight training, I have had structural problems (squat especially) for years, and by working through it, I still haven't over come it, and my training has had serious limitations because of it."

Hey man, I think we have all been there and experienced the same things that you are going through. I still have major limitations because of flaws in my structure.

"But there has got to be some trick to getting closer to a more balanced stance."

I'm sure you have heard of the concept of the 6-Harmonies?
The 6-Harmonies are 1. Hands and Feet together 2. Elbows and Knees together 3. Shoulders and Hips (on both sides of the body = 6).
You mentioned your feet. One of the big things that has helped me is making sure that the toes of my foot are aligned with my knees, this may help with the squats.

"I have to admit, the more I learn, the more I see how much I still haven't learned, and sometimes it feels like perpetual failure. IMA is hard!"

Sounds to me like you are on the right track and on the edge of a breakthrough with your training. Stick it out! Darn skippy IMA is hard. Thats why we love it, right?