I would be inclined to make sure you're not road riding after 5:00 (happy hour, I'm not kidding). We've never had any troubles with discourteous drivers, some will give you an extrawide berth if they can.
I imagine that the Seven Mile bridge might be a little daunting. There's construction all the way at the top at Florida City and I don't think there's any way around it.
I have see fully loaded tourers riding on RT 1 before though, so it can certainly be done. Not for the faint of heart. You'll probably need to hear advice from someone whose actually done the trip though.
Stop at Geiger Key Marina if you go. 1 1/2 miles off of Rt.1 down toward the southern end. Great place to "hang with the locals". In Key West, hunt down the Green Parrot, another "locals" place.
Florida really needs to step up to the plate on this issue though, it would bring some decent revenue to the middle keys. Since we drive through the keys, we've seen the spots where you wonder "Why haven't they put in a trail here?" because it looks as simple as putting down blacktop.
Oh, if you start at the top and go down, the wind will be at your back.