And horizontal slices result in cut fingers!!!
I think the reason the dinner plate sized thin pounded chicken "poofed up" was that the pounding just stretched all the fibers out and when the cooking heat was applied the muscle (a chicken breast is in essence just a big muscle) fibers tensed up and contracted due to the heat denaturing the proteins. I've seen steaks plump up a bit in cooking and I think the big reason the chicken plumped so much is that it was just an extreme case, so thin and spread out, no real structure to resist contracting. That must have been about 1/8 inch thick!
When I consider solutions I think scallopini, which I often see at the butcher's shop, thinly sliced rather than "you pound them at home." I've often flattened chicken breasts for some dish or other (e.g. au poivre) but I've never pounded one out to a dinner plate size! I've been content with the shrinkage that usually occurs.
I presume you wouldn't have wanted a dinner plate sized serving so you must have been intending to accept some shrinkage and the problem was that you got too much. I think rather than pounding thin and hoping it will stay thin that you should turn to slicing thin. I think the pounding accentuates the plumping up that follows when cooking.
So what I would suggest is thinly slicing your breasts, either on the diagonal which is a reasonably safe and easy procedure, or splitting them horizontally, or have your butcher do the job for you.
It would be interesting to hear details on your intended end result DL. It's always so much fun to hear about what other people are trying to accomplish in their cooking adventures.