I've always felt that the obvious way to fix stroads is to separate the two functions: the road and the street function. And for that, the ancient Dutch concept of the ventweg seems like a good fit. A road in the middle for through traffic, and a street on the sides for access to all the businesses along that road. They connect at the major intersections. It does mean that if you have to get to a shop on the opposite side of the road, you first have to go to the next intersection and then turn back, but in the mean time all of the through traffic can continue without interruption.
And if you then combine that with the Carmel-style intersections @yudderick pointed out, you've got a really nice solution.
But maybe first make sure no new stupid stroads are getting built.