hey ! thanks for advices... haha it sounds 'easy' with HR (I wear HR strap and i have power meter), but the whole point of riding a bike is to GO HARD
so hitting 100%HR at the end of 10-15 mins climb is what I like (if legs are fresh).
but then, short climbs are too short to experience back pain. It happens on hard >20 min climbs - it's diffcult to keep high cadence on 1h ~8-12% climb
and yes, i can try to go slower (and also standing - which gives some relieve) on easier climbs - but this is not a point in climbs
probably my back is arching down - tight hip flexors?
I'll focus on stretching and training core muscles like all you recommended (deadlift, kettlebell swing, some other core related - like side planks with some movements etc.)