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Would be beneficial to have someone take a look at your squat mechanics as you can sometimes make small adjustments with heavier weight that you may not even be aware you are making.
Working at your upper limits these things will occur to everyone.
You will find you use different tools for different areas. Some for more than others.
For the psoas use a playground ball.
Different way to hit the Psoas
Bubo Barbell Pec/Psoas Smash Quicky or What to Do With Those Bent Barbells
Jill Miller Smashes Your Guts! (and psoas, and tacked down viscera, and matted down abdominals…) Part 2
Episode 301: Psoas Flossing and Biker Hips
Episode 129: The Twin Bowstrings, the Psoas and Scalenes
Episode 75: Your Inside Psoas Bits, World Record?
Episode 40: USAW Oly Prep: Some New Hip Love /Psoas/Calves
Episode 26: Hips and Seppuku: Psoas and Hip Soft Tissue Mob