Another option (my current setup), if you fly other sims besides BMS, to the minimum €730 VirPil Hotas with the F-18 grip. If you want the F-16 grip you can get the Virpil WarBrd stick base (€190), then a TM Warthog Throttle (€240). and the TM f16 stick (€160) for a total of €590 here. You set the PID/VID of the JStick to match the original TM Warthog and your system and the TARGET software see it as a standard Warthog. Then you simply run the 128 DX TARGET profile (it only targets the throttle) and every switch\hat\button position is seen as a DX press. Unfortunately BMS does not currently see DX33-128 so no matter what the solution you would need to use Oak’s suggestion of VJoy\Joystick Gremlin to create multiple 32DX devices for BMS, or whatever VirPil’s solution is. For BMS I simply disable the TARGET profile and Alt Launcher has all my switches set for press\release so it is not an issue. The cost is only slightly more than a stock Warthog HOTAS and the VirPil stick base is exponentially better… and if you want sell the OEM Warthog stick base over on the Cougar forum to save another €50.
Edit: Sorry Bayonet, I see you have already purchased your gear!