"What do you propose a well-educated rider should do, when all the bike lanes are in the door zone and bikes are legally required to stay in the bike lane?"
Well that's the usual poor planning I see in America. Sharrows or "share the road" signs are much better than many of the dedicated bike lanes I've seen here.
First, find another route, if possible. Second, start going to your city's public meetings and/or complain to the city about the clear danger that poorly planned bike lanes inflicts upon the public. Learn the law specific to bicycles for your area and get involved with a bike advocacy group if you really care.
As far as helmets go, I like to keep my brains intact, so I wear one, and have the abrasions on an old helmet to prove it. Front tire blowout and dumping at 45 KPH downhill on a recumbent was an experience that could have been worse sans helmet. That said, a pound of plastic and foam can only do so much for you. Good luck!