I am moving from New Orleans to Chicago and I have a 10" thick foam mattress. When they brought the mattress to my apt for delivery it was in a vacume sealed bag which would really reduce the space needed to move. I am trying to find a service or somewhere I could get a bag that I could vacuum the air out and move it.
You can try Home Depot or Lowes for them.
If you fold over the mattress and wrap it in plastic, seal as much as you can leaving one small opening and then use a vacuum to remove as much air as possible, then fold up the mattress tighter and remove more air with the vacuum. Get it as small as possible and rewrap it so it doesn’t expand. I don’t think you’ll find anybody, but contact packaging/shipping stores, see if they can help.