>I wonder if it'd be possible to stuff and roast a woodchuck -- and
be
>able to chew any of it when it was done.
Sure, if it's a young one. I'd use a very moist stuffing, one with sausage in it perhaps.
>I think I could keep it from drying out -- with six or eight layers
>of cheesecloth over the top, a fairly copious basting liquid
The usual practice is "barding." This is placing sheets of fat (e.g., beef suet cut thin) over it and tying them in place with cotton twine. That provides basting and moisture. I have occasionally done a very lean venison roast with the alternate technique of "larding," which is threading strips of fatty material throughout the meat. You use a special tool for this, a "larding needle," obtainable at kitchen shops; and the wonderful word for the strings of fat is "lardoons." It makes a real difference in the juiciness and flavor, believe me. Larding or barding can be done with salt pork (what I used in the first go-round on the venison) and/or suet.
>(replenished ad hoc), and frequent bastings
>-- but I'm not so sure it'd ever soften up . . .
I'd also do it in a closed cooker, like one of those Romertopf clay thingies with a glazed inside. Basically you would braise it to death. It would soften up, if you used a young animal and cooked it a while. Try it with an 11-pounder and you'd be chewing it for a week.