Boxing in the chimney - in my opinion - will not solve the problem (It may help, but not fix). The air is being pulled down by negative pressure and you have to solve that.... No, the interior double wall is not making the problem worse.... In bad situations like this, I would usually see if the customer can install an interior T right near the wall. This allows you to open it, insert a piece of newspaper toward the chimney, and therefore have a better chance of reversing the chimney easily. Once reversed, Elks advice about a really hot startup will warm the chimney and keep it drafting. I wonder if a temp outside air hookup - just to test - would work. Like a piece of plywood with a 2" hole cut in it that inserted into a partially open window and then fed right to the stove air control. At least this might give you some indication if the air was off-balance. OH, you mention the force at which it comes down. If you install the T and then stuff a piece of newspaper in there balled up - that slows the downdraft a bit before you light it..... That makes me think that some kind of a solid turn damper would help also.....to slow or stop the reversing when the stove is not in use.