I bought some cheap Whitin ones on Amazon that have a wide toe box. Now that my gout is mostly under control they are my gym shoes, but back before I got it under control they were the only ones I could get on when attacks happened.
This was the only shoe I could wear for that last maybe year before I went on Allo. Unfortunately it is no longer available but it might give you an idea. I still use it now as my gym shoe. Main thing is a wide toe box and no laces. I have another of their shoes with laces that I could never wear with gout even though it works fine now.
Shoes with a wide toe box. These are the only ones I could wear reliably.