Caveat: I've felted over the years but I don't consider myself a proficient felter.
I don't see why you couldn't do as you suggested, although it might be easier to needle felt in a container instead of wet felting since it would be more difficult to manipulate the fiber when it was constrained in a container.
To felt another piece on top of a felted mat, I would loosely needle felt some fiber on top of the felted mat to give the next layer something to grab on to.
If you are wet felting the second piece on top of the felted mat, your felted mat may "full" more (shrink and become more dense).
Folks use 'felting' & 'fulling' interchangeably however there is a difference.
Felting is when you use locks of fiber to create a solid piece of fabric.
Fulling is when you have a piece of fabric (felted, knitted, crocheted, woven) and it shrinks and becomes thicker.
Have you looked into needle felting? For doing batts, you'll want a tool that holds multiple needles like this:
This is a "Pro Tools 10 Needle". I believe HalcyonYarn & FeltingSupplies.LivingFelt both carry it. I haven't ordered from either of these folks, so buyer beware