It can be done and, in fact, gen 4 5.3's run the flat pistons with 243/799 heads and retain the same c/r as yours had stock. If all you're trying to do is increase c/r then I'd think the easiest and cheapest way would be to have your heads decked... that way you don't have to deal with balancing.

If you're considering a cam later then flat pistons + 243/799 heads will give you a great starting point, but because of the larger valves you'll more than likely need a stall otherwise you'll be a turd off the line. A cam with a larger split can make up for it somewhat, so I'd consider a 208/218 or 210/218 with .500ish lift and I think you'll be happy with your fuel economy as long as you don't get stupid with your LSA.