It is very, very uncommon to see someone with a true leg length difference. So I would want to make sure that this is not a pseudo LLD which is really a malalignment in some way of the pelvis/low back area. You also seem to have overactive hamstrings which might also relate to the same.
It's true you might have some local patella issues but this does sound a touch neurological. I'd get someone to look into the low back region, even have some deep tissue massage in the area. Keep wearing suitable footwear for running and see what happens.