Welcome to the EGGhead Forum - a great place to visit and packed with tips and EGGspert advice! You can also join the conversation and get more information and amazing kamado recipes by following Big Green Egg at:
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.