Hi Dave, welcome to our little community.
I have the little brother to your weber one touch and I use that for all my quick grilling, I love my little weber. If I may though, a couple of tips. Steve mentioned indirect cooking method and Al, (Dr Sweetsmoke) mentioned using the lid. The way you're describing the fat from your burgers putting out your fuel, it sounds to me you're BBQin' the same way I used to, allow me to explain.
3 Yrs ago I didn't BBQ,(although I thought I did). I spent my time flipping and turning, going through fuel like there was no tomorrow and thought the lid was there to keep the spiders out when I wasn't using my BBQ. Give this a try...
Instead of covering the whole bottom of your BBQ with charcoal, load it all on one side only, make sure the bottom vents are open.
Put your food on the grill on the opposite side to where the charcoal is (this will stop the heat burning your food)
Whack the lid on (with the vent also open) and chill out.
This is what Steve meant by indirect cooking. Like Al said, it turnes your BBQ into an oven, the heat circulates around the inside of your BBQ, through your food, and cooks it instead of burning it.
The long and short of it is; constant flipping and turning is no longer necessary, more time to socialise, better tasting food. If you really wanna be flash, get hold of some BBQ smoking chips (apple wood is lurvely with good quality burgers), throw a handful on the charcoal same time you put your burgers on and for that charcoally finish give em a quick flip directly over the charcoal just before you serve. I find 20 - 30 mins is sufficient to cook tesco premium bbq burgers.
Happy 'Qing
