Yep, by 'hip circles' I mean trying to open up your range of motion in your hips by doing circles, tilts, figure eights etc. The idea is not to just go through the motions, but to actively try and (gently) push your range of movement limits. You can do these standing up, sitting on a ball (Chek), etc.
Did anyone mention if your hips being tucked under is abnormal? Any discussion as to a remedy (my thoughts would be 'hip circles')? If it's normal for your body, it sounds odd to me that you should have to compensate by curving your back all the time.
As for compensatory movement, it's about putting in some work to balance out the load across your joints. If you're always curving your back, then you may be developing some tension in the area or some other alignment problems.
I've attached images from a Chek article "Fear the Squat No More". I'm referencing him because you've had some contact with his ideas before.
His thoughts are that you can lose spinal fluid through chronic curving of the spine, and arching is needed to compensate.
That aside, it will help stretch your back muscles out if you do some arching work (unloaded).
You could do any number of bending exercises - something a little closer to home than a Chek squat might be the pull-through.
I'd be starting unloaded and after you've seen some improvement, advancing to a very light load. Keep the emphasis on stretching and elongating your spine.