I'm sure you can find one of the blue and white striped 4" thick lumpy mattress we had on ship at the closest DRMO or surplus store Senior Chief. I bet they'll throw in the stains for free. Should fit without a problem. Show the wife how we slept in the good old days. Stow a couple girly mags, a few letters from home and press a set of liberty dress blues underneath to complete the illusion. You could even have air bedding days on every other Thursday! Think of the fun if you can find a few of the chicken feathered pillows we were issued!
Back to the real question - it's going to depend on what you get as a replacement. I replaced ours with a 6" foam core. Very comfortable and has shipped rolled up and compressed down to a 6' x 12" cylinder (short queen). Once unpacked it expanded to proper proportions. You could always try a dress rehearsal with the old mattress. If you can get the new mattress in but not the old one out you can cut to old one up into manageable pieces with a saws-all. Might make a mess but a proper field day before liberty will square everything away and keep the LPO happy.
Cheers shipmate.