I asked a human physiotherapist about this. They said it could be a ligament injury. Those can heal unless its a completely torn ligament, but it as a rule takes quite some time. It doesnt seem to be a complete rupture, because he retains such a lot of function. Its very promising that he has so much function.
Another possiblity could be an elbow injury. That could explain why he wants to stretch the arm out under him when he is “loafing”, and why he has trouble getting up after flopping.
There could be a hairline fracture somewhere, which x-rays could confirm, but you wouldnt do much about it in a rabbit. You can put a cast or a splint on a rabbit if needed, but rabbits often remove casts or splints. If there is a fracture, it could be wise to not let him jump or run on the stairs for a limited time, so a break gets the chance to heal.
Physio also says arthrosis as a rule hurts more during rest than during moving.
The antiinflammatory med I assume is meloxicam? Meloxicam is both an antiinflammatory and a painkiller, so even if you havent seen improvement, they could still be helping against pain, which is very important for rabbits as they are highly sensitive to pain.