I do normally clean the whole thing completely as you suggest.
But this is the first time I used an epoxy primer.
By the time I was done, I went to clean it out and I couldn't get much of the primer out.
All I had was mineral spirits and naptha. They were about as useful as water.
Perhaps it wasn't so much what I was using to clean it, but instead maybe I waited too long and it began to cure in the gun?
Either way, I'll use lacquer thinner next time.
Thank you everybody for your advice.