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i would say that you should get an MRI. X-rays only see certain angles, usually front or side and it is easy to miss disc bulges in other directions. An MRI would be conclusive.
it would seem to me that you have a disc issue, which flares up during spine flexion. the easy thing to say would be to train for neutral spine during surfing but it is probably easy to say and less easy to do in the water.
i would say to work on hip flexion with neutral spine. there are some good banded distractions to help with this, like the hamstring floss with band going out back. i would also work on putting the hip socket to the rear of the socket. it may be biasing forward which reduces flexion capability. hip openers will also help and when you bend over, you may want to practice good squatting technique (ie. not knees in, torque the feet) which will enable to you to maintain a good bent over posture versus encouraging flexion to maintain bent over posture.
breathing is a big factor – people undervalue too much what diaphragmatic breathing does for stabilization. work to achieve belly breathing 24/7 and especially during the excitement of being on a wave. this helps you maintain proper posture with less effort and make it reflexive versus conscious.
as for sitting on the board, you may want to practice rolling your pelvis forward while sitting. if you let the pelvis roll back, this will encourage spinal flexion. you can practice this in a chair. sit, then spread the legs to wider than shoulder position, which is probably about the width of your board. then stabilize, and bend over at the hips. press your pelvis forward, as well as maintaining your spine shape. you may not get very far at first. mobilize a lot and practice this. then when you’re sitting on the board, put your arms a bit forward on the board to support and roll that pelvis as far forward as possible.