New here so hope this isn't too old to give a thought to, or perhaps you have the issue sorted out by now.
I have a similar problem with quick steering as well as riding a bike being very good at finding old injuries, however my issue is more due to seat shape not allowing me to move back so feel a bit 'stuck' in place. (older sports naked!)
One of the things I did to alleviate back complaints was to consciously bring my elbows in. Obviously, effective steering is taught to us by being horizontally parallel to the ground but when I am in this position it niggles in places. I am naturally tight across the chest so by squeezing my shoulder blades/opening up my collarbones it allows the elbows to come in, and are then actually below the horizontal - which means I can come up slightly into a more comfortable position. Think a boxer in the 'guard' position, with hands covering the head and elbows tight, protecting the torso is the way I visualise it.
I do have to make an effort to think about it when I'm riding but definitely works for me. But, different bike, different physiology but just thought I'd share...