I'm about the same size patty as you (7 oz) and I find that 550* normal height for about 3 - 4 minutes a side, depending upon how cold they were before going on the grill, and they're done. I cook to closer to 130*, so figure 5 minutes a side to get to 160*.
I sear my steaks open lid on spider similar to what you do. I let the fire get roaring open lid and sear open lid. I can then shut it most of the way down (i.e. bottom vent about a 1/2" - 3/4" and DW holes open) and hit 325* for roasting without having to remove the food and wait for the egg to cool down. Might be worth a try if you have to make burgers under a time constraint.