Slow cook the turkey overnight or cook superfast?

Slow is always best. When proteins cook too fast, they tighten up quickly and more moisture is squeezed out in the process. Slower cooking allows for more gentle coagulation of the proteins, thus moister meat.
Brining your bird is one option for aiding in the cooking process. Another is deboning the bird as smaller things cook faster than larger things. Heating up those bones is wasted energy. Also, not stuffing your turkey means there is less mass to bring up to temperature so the cooking takes less time.

You can cut your turkey into it's parts and roast it in pieces. You don't get the presentation of a whole bird, but you do end up with turkey that's more evenly cooked (you can start the dark meat before the light).
You can also cook the turkey unstuffed which should decrease cooking time.

My Mom always cooked her turkey the day before Thanksgiving. She carved it, put the meat in a pan and poured some turkey broth over it to keep it moist and into the refrigerator

When she was ready to serve she put it in the oven to heat up and was good to go.

When I was younger it drove me crazy but now I appreciate her approach. We had a wonderful, unstressed time. There was room in the oven for all of the great side dishes and it was a pleasure to clean up afterwards without also having to deal with the turkey. I don't have the courage to go that route yet - can't stand up to the turkey purists in the family.

Check out Williams sonoma turkey two ways recipe. You break down the legs and thighs from the body and confit. You could do this the day before. Then cook the breast separately, much shorter cooking time and then crisp up the confit legs.

Do everything night before. Put celery bottom of roasting pan, rinse and dry bird inside and out,salt inside, stuff, use Reynolds turkey oven bag, butter top of turkey, bird on celery in bag, c
In refrigerator for night, put in oven am, set time to cook. Ready for sides. All set-yum.

Deep fry it - after brining (24 hrs) and dry refrigerating (8-24 hrs) it. This does require care and near constant monitoring, but a 15# bird is done in about an hour.

If they are arriving as early as 11 AM, sleep late, then ask them to help out ;0)

There's a recipe on Cook's Illustrated, for a 12-14 lb bird, where you brine, chill, and butterfly it ahead of time (you'd begin 16-24 hours before roast time) and roast in just over 2 hours. I am going to try butter flying the 'extra' turkey this year.
http://www.cooksillustrated.com/recipes/detail.asp?showFullSite=true&docid=5116

How big is your turkey? I've always had good results cooking relatively quickly (when I say 'I' I mean the one turkey I cooked solo... and all those I've assisted my dad with, of course) - about 12-15 minutes per pound for a stuffed bird. I can't think of any way that it could go faster without it still being raw in the middle but maybe others have other ideas. You could always not stuff it if you really need to speed it up? Unless you have a monster turkey, though, 6 hours seems like a long time. Can you start it a bit later and then just eat an hour or hour and a half after they arrive?

Generally speaking it is not advisable to cook a turkey below 325, but perhaps others know of a technique to spread the cooking over a longer period of time?