My opinion is that you already have the right oil viscosity, 5W20. I have a similar truck ('05 F-150 5.4L), by the way, and live not far from you, so I think I understand your needs.
You didn't say which oil brand you use. Fords are pretty happy with the Motorcraft brand and it's a good value oil, so it doesn't have to chew hard on your wallet. You can, of course, go higher up the food chain but I wouldn't count on that being a cure in your situation. Make sure you use a Motorcraft filter, or any other that has a good anti-drainback valve (ADBV). The Ford modular engines are prone to various rattles on startup, not all of them worthy of a great deal of concern, IMO, but a good ADBV is vital and the MC filter has that. Again, it's a good value product.
Yeah, six miles is a pretty short run, especially in the winter. If the truck lives outside, you might want to consider a block heater. It will drastically cut warmup time and extend engine life. This may be the best answer overall. Any oil will be stressed in your scenario. Condensation and fuel dilution can kill the best oil, so in your case, the old 3000 mile OCI is probably one you should follow if you make no other changes.
One almost free thing you could do is to make a point to drive the 469 loop once a week and cook out all that condensate and fuel dilution. Also, in the coldest part of winter, you could partially cover the radiator with cardboard for a quicker warmup... but you'll have to remember it's there!