Unfortunately there isn't a definitive answer. Some people with UC who have surgery have said their EIMs have gone away after surgery, but others have had ongoing problems even after surgery.
I'm actually in a fairly similar situation to you, except I still have my original rectum and not a j-pouch - but the rest of my colon has gone. I don't go as many times a day as you do, but the urgency, abdominal pain and EIMs are all wearing on my nerves. I would go back to having a stoma tomorrow, if just the uveitis alone was guaranteed to disappear. But as it stands, I'm not ready to make that decision (that is partly because of uncertainty about
future medical supplies, presumably a worry you don't have).
I'm sorry I can't help you to come to a decision. But I do think I'd rather have a stoma than be going 15-20x a day. You're likely to feel better within yourself if you get rid of the existing disease too, even if the joint pain doesn't disappear. PS: This may be obvious, but rule out any small bowel disease thoroughly first before deciding on reversal surgery.
Dx Crohn's in June 2000. (Yay )
Tried: 5-ASAs, azathioprine, 6MP, Remicade, methotrexate, Humira, diets.
1st surgery 20/2/13 - subtotal colectomy with end ileostomy.
2nd surgery 10/7/15 - ileorectal anastomosis. Stoma reversed and ileum connected to the rectum.
Current status: Chronic flare. Do I have any other kind?
Current meds: 50mg 6MP; Entyvio (started 3/11/16)