Do kilts have a "break-in" period?

[flyrod6057]

What's weird is that when I lay the kilt open and look around the edges of the lining, I can see the very edge of what appears to be a stabilizer underneath. The lining is black, but there is a layer of firm tan-coloured material below it, which I would assume is the stabilizer.

You may be correct here, or possibly not. There should be two internal parts in the back: A piece of hair canvas interfacing, and a stabilizer. What you're seeing may be interfacing... The stabilizer could be made of the same thing, or the kiltmaker could have used a different material altogether. Hard to know without a little exploratory surgery.

How difficult is it for a kiltmaker to take the lining off, evaluate what's below it, and (possibly) stitch a stabilizer in place?

Removing the liner, evaluating what's underneath, and installing the stabilizer is a relatively simple task. I don't know what a kiltmaker would charge; it's mostly labor that you'd be paying for. (If you were nearby, I'd do it for a pint or two at the local pub!! ...but I'm not a professional kiltmaker...)