I've found that the best way to get better mobility is to simply spend more time in the positions you want to improve.
If your overhead squat mobility sucks, grab an empty barbell or light load and spend time in the bottom of the squat. Get active and hold for 10, 20, and 30 second sets.
If your shoulder mobility sucks, hang on pull-up bar more. Or grab a barbell and hold it overhead with a tight core and active shoulders.
If your front rack sucks, put a barbell on your shoulders and actively work to drive your elbows up.
And if you feel pain, stop. But a little discomfort is to be expected. Changing the body takes time. I found that endless foam rolling wasn't nearly as effective for me as pushing my current range of motion in active drills.
Photo 📷: @tbolte101 - Taylor was looking to improve his comfort level in the bottom of his overhead squat, so we spent time in the bottom of the overhead squat 🙃