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The core is connected up quite intimately to the whole digestive system and when nerves reorganise there it can get funky indeed.

That said, try hanging. Not necessarily pull-ups... though while you're at it might as well do some negatives at least: jump up, let yourself down as slowly as possible until you get that rotation in the shoulder and then you are hanging properly. Then stay there, move your legs, explore the load shifts, such stuff. That's going to tickle nerves that you might never have tickled before, but which need occasional tickling or your whole back gets confused because we happen to be monkeys and hanging from stuff is in our biomechanics, the nervous system expects those kinds of loads. Generally works miracles when it comes to back issues, and core issues are often just reflections of that.