I don't have an answer, but I do have kind of a similar problem, where BMS just won't recognize one of the HAT switches and the k-switch on my X-65 throttle. I couldn't find a concrete answer, but I was under the impression that there was a hard limit to the number of DirectInput buttons it could recognize. Also, the BMS setup menu apparently doesn't recognize DX shifted button presses (though they work in the sim), so these have to be set up by hand in a key file.
The only way I found to sort it was to use the profiler to convert those buttons to keyboard input, though this is something I prefer not to do in general if it's avoidable (mostly Saitek
's fault for having crappy software). I'm sure there are many Warthog profiles (and key files) available, perhaps you should just look into using one of them?
For the moment, I've chosen just to live with it because I'm only willing to screw around so much, everything else works, and the X65 throttle is bristling with other HATS almost to a fault (though I'd rather pick different ones not to work if I'm limited).
Good luck sorting your issue.