You'll see references to first allowing meats to come "up to" room temperature before placing on a grill. (You won't be leaving it on the counter long enough to grow bacteria.) Think of it as "free heat" for your grill, and "free A/C" for the house in summer, as the meat slowly comes up in temp on the countertop.
That being said, I think the real issue is as Foster identified: not enough heat. Burgers don't take long, so have coals "enter the grill" close to ready-to-go temp, without regard to how long they'll last (since it should be a short cook.)
What's good about putting lit on top of unlit is that you get a longer burn at whatever temp you began at. New coals catch as old ones begin to die out. You see it all the time with smoking "low and slow," in either a kettle like yours or in a smoker.
You have plenty of capacity for heat in the S'nS but I think you set it up for more of a long, lower cook than would be ideal for burgers ... UNLESS you were going to cook them direct, and were doing several batches and needed the heat to remain a long time. You'll get it!