Fitted diaper with stretch polyester outside????

I think you can use anything as a fitted! Peruse this website:
http://www.timelessspirit.com/NOV04/stell.shtml
I have a bunch of material that is a polyester knit that I use to make fitteds. I just make sure that the softest, most natural fabric is against dd's skin. Works great for me!

I'm interested too. Does the polyester make it waterproof at all? How would I help the not-stretchy cotton inner work with a stretchy outer (I like the stretch idea)?

I think it would work fine. In my experience, it doesn't always work great to mix an inner stretchy layer with an outer non-stretchy layer, they just don't match up quite right. Your idea is the other way around, but I think you might have the same problem. (but maybe not, you never know). To be safe, I would match stretchy with stretchy. Try using cotton t-shirt fabric for the absorbent layers of your diaper. Or you could use cotton velour, it is stretchy and so comfy against baby's skin! One of my personal faves is stretch terry, which is what those baby bath towels are made out of. You can find a lot of those at the thrift store (just make sure it is at least 80% cotton).

I don't know how well the polyester will repel moisture by itself, but it definitely won't hurt!