I also host a large extended family most Thanksgivings. My method is that I do the complex cooking (I smoke a turkey, and one or more side dishes). After dinner I start making a stock with the turkey carcass (seriously, there is nothing better than turkey stock from smoked bones). The whole evening, I'm either doing cooking "things" (sometimes faking it), or cleaning dishes or tables or something. I'm always moving, but I'm not verbally interacting a ton. It works surprisingly well for me.
Damnit! You beat me to it!!!