I have moving gout like you. I found a cure with diclofenac. My first attack lasted 3 months and was hell. It was never diagnosed as gout as it started in my ankle and moved around. Only a kindly nurse had a suspicion it might be gout and prescribed it for me despite being diagnosed with a sprained ankle.
The diclofenac cleared it in 48 hrs. Might be worth a try. It has negated my gout attacks. I take it only when i feel an onset and then it goes within 1-2 hours. If it’s a strong attack that comes on during the I night that means I cant walk when I wake up I might need 3 pills taken about 4 hours apart and then next morning I’m fine. My doctor just gives a box to keep if I need one or 2.
Without it my attacks last 2-3 weeks.
Changing my diet had no effect for me.