maybe you could use a power sander instead (those random orbital ones, I have read that some people use them to felt large pieces).
I've used the one that goes back and forth super fast, but not an orbital one.
I'd be worried about the wool just swooshing around in a circle!
But yep, that could help.
I tried "nuno felting" a rubber mesh into felt using my sander.... to little effect.
I put it down to the fact that unlike fabric, the rubber couldn't shrink with the fabric. I have a feeling that you'll have the same problems with wire mesh, but the holes might be bigger and help to fix your problem.
Hmm, or if you needle felted it slightly before wet felting it might give it enough grip.
If you do try it, let us know!