When I have had to clean a gun case I have just used water and soap and then let it air dry. It has worked for me but I don't know if it will work on super plush fabric, as the ones I have used have been standard padding on the inside.
A while back I bought a couple very nice soft cases at an auction for next to nothing, problem was they smelled like an ashtray. I actually ran them through a cycle on my wife's front load washer. They came out clean with no ill effects, but your results may vary.
How do you figure? I use soft cases for trips to the range, they're much easier to handle than hard cases. I've heard of guns rusting when stored in hard and soft cases.
Run them through the Washer if their Synthetic Fabric. Hang them open to dry. Spray the interior with silicone before using. Been doing that for years with cases for Hunting that tend to get dirty.