Yes, I'll take the shroud off tomorrow, clean out the ashes, and see what I can see. I seem to remember reading a post about another BK insert owner where the screw holding the shroud on was preventing the thermostat flapper from moving? Hopefully that's what's happening here, as it's an easy fix.
Verify that the thermostat flapper is free to fall closed when you choose full low. It has been known to be jostled out of place.