I would say go with your gut. There is a road I live nearby that I will not ride after 8 a.m. If I want to ride that loop, I get up at 4:45 a.m. and am on my bike by 5 a.m. I see people ride it but to me, recovering from a head injury isn't worth it. And you aren't being a sissy about it. I have gone over the handlebars many times in the dirt, but I'm not really so willing to do that on a road with cars behind me. I was pretty sketchy about riding on the road, but I have to say drivers in this part of Mass anyway are not that bad. There are some bad ones, but the roads I ride on are not that heavily traveled. Maybe you can use googlemaps and find another route? Talk to your LBS too, they might have some insight as to where you could park or a safer route.

Everyone gets obstacles like these, don't give up. I sometimes drive and park at a shopping center. I park the furthest from the stores. There are no signs that say "customers only" or things I see at my other home in Tahoe. There I'm not sure I would try it because tourists tend to park at supermarkets and go skiing! Just don't take the space that is prime like someone else said. Maybe you know someone that lives on this route too and you could park at their house? I would say most of all, the church would be a good bet, but I would ask on that one.