It sounds like what you are describing is the same as a Kingussie pleated kilt, only with the knfe pleats facing in, towards the center box pleat, rather than out, as it was done historically.

No reason why that would not work - that's actually how Utilikilts are pleated.

I suppose you could reverse the twill on one side of the kilt, by joining your two pieces of tartan right-to-wrong side. But it wouldn't actually be symmetrical, like you think. The center pleat will be your box pleat, and you won't want a seam running down the middle of the outside of the pleat. You'll want the seam hidden inside a pleat, which means it will actually be a bit off-center.