Update: the new route is 3.5 miles one way, and much less stress. Has a bike lane most of the way, and fewer stop signs and traffic lights. I was feeling a bit stupid - why did it take me so long to try this route? And then I remembered - I had tried it before, but a new hospital was being constructed and that made the route undesirable (debris along the side etc). All that is over now, and the ride is much more peaceful.

So like many of the traffic related threads on the commuter forum, this ends with a find-a-newer-longer-route solution