We've been doing smoky burgers for years. We buy grnd beef in chubs and slice the chub while still wrapped. We slice them about 2" thick then flatten them a little (a tad thinner in the middle) after we unwrap them.
We smoke them a little more rare than we like to eat them so that they'll be perfect when we reheat them. After they cool down. we freeze them stacked on top of eachother w/ 2 pieces of plastic wrap between them. It's kind of like re-assembling the chub once they're cooked.
After freezing, they're easy to separate w/ a good stout knife. You can heat them in the microwave for a quick snack, grill them over charcoal, or even throw them back on the smoker for another round of smoking.
One quick trick for extra flavor, put them on a rack directly below a fattie, some ribs, smoked sausage or whatever and let them get dripped for extra flavor.