Well you will have to subtract those too because it take up space too so by subtract the woofer displace it might not be 28 cub. Seem to me you got enough room for those 4 18 sub. It gonna be hard to figure out if that box tune on what you want. I can still calculate with the 28 cube. What's the external dimension? Are you using 3/4 MDF board...
I have use contact cement but i don't think the water base are good for the carpet. I think are different kind of contact cement. The one that look kinda caramel's good. The contact cement water base Might be good for fleece because i use thos and it stick hard. You can trying using 3m spray adhesive..