To the best of my knowledge, the flooring we work on is concrete. Over that, they layed stips of 2" by 2" and nailed that to the concrete. These were spaced 2 to 3(?) feet apart so that the 3/8" plywood on top would have some give. Next, 2" of a nice spongy foam was put down and a commercial grade carpet on top of that.
It's not the prettiest thing in the world, but it's easy on the uke and durable.
Just a thought: I wonder if Zebra Mats would have any recommendations of their own on what to build under their mats?? Might e-mail them and ask.
Have a good one and good luck!