When I got the new to me van, it had coffee stains on the seats. I used upholstery cleaner and a powerful shop vac to get the stains out. Scrubbing with soapy water didn't work, but a bit of scrubbing, then a short time to let the cleaner work on the stain, then the vacuum got the stains out. A couple of them were pretty ugly and took a few rounds of this. It took some time, but it was worth the effort.
I would expect that technique to work fine on the inside of a case, so long as you don't get overenthusiastic about getting it all soaking wet. The key seems to be using just enough liquid and vacuuming all of it out if you can. Then letting it air out for a while.