Brian,
I would think the application you describe is perfect for retreads. The airlines probably go through them so fast the sidewall deterioration is not an issue. If the core tire passes the retread manufacturer's QC requirements the tread will likely be used up by the airliner much sooner than the sidewall deteriorates. But, on a little GA plane that sits in the sun with relatively little use, it seems likely the old sidewall may fail before the new tread ever does.
By the way, how long does a tire last on an commercial airliner?