I did just what you're thinking about; I had my 'smith rechamber my 243 to 6mmRem AI. I had exactly the problems naedlaen brings up.
If you're trying to decrease/eliminate stretch in your brass, I suggest staying away from max loads. Then, get yourself a collet-type sizing die, and size the case necks only, just enough to grip the bullet. You will need to figure out just which size collet will be needed to do this. Remember, cases blow out to fill the chamber at the instant of firing, then spring back after the pressure spike, about .003" overall in the diameter dimension.
If you have the tools, or are gung-ho enough to get them, you may be able to take 308 Win cases, neck them down to 243, then fit them to your chamber by turning the necks down, or reaming them, so you get a "tight neck" situation, resulting in a fired case that doesn't need sizing, or only minimal sizing, to grip the next loaded bullet. A significant amount of luck, in terms of your rifle's chamber dimension and the wall thickness of the necked-down 308 brass, will be needed for this to work. And, it might all be for no real gain due to the handi's inherent flexing.
I strongly advise against going the AI route.