You're probably not going to get much if any penetration in that kind of time frame. Brining/curing a ham takes a while because of the density/size of the meat. 8lbs would be about a 4 day cure, and if there's a bone, you'd want to inject around that. I'd suggest you just freeze it until you have time to do it up right, if a ham is what you're really after.
An overnight rub in tenderquick probably won't cure it much... 8 hours low and slow would give you something more akin to pulled pork (if you cook it to 200ish...) or just sliced roasted pork if you don't. You won't see that pink ham color because the nitrites can't do their thing in that short of a time. Then again, I don't use tenderquick for cures, I usually use Prague Powder #1, so I could be wrong. Just speaking from what dangerously little I know about the curing process... I'm sure someone with more knowledge will come along ..
YOU WANNA THROWDOWN?
You should! Fun and fabulous prizes await you!*
I have a bunch of stuff that cooks meat outside using some form of combustion.
*Actual prizes may not be fabulous. It all depends on what your definition of fabulous is. You're not going to win a car or anything, so don't get your hopes up. Just trying to give you realistic expectations.