Have you tried just using Hauptwerk's built-in recorder to record the MIDI data? Playing back should then give you exactly the sound you heard when recording.
Make sure that “Arm audio recording” is UNTICKED, and “Arm MIDI recording” is TICKED, then click on the red RECORD button, and off you go. Be aware that if you do this Hauptwerk will start by doing a General Cancel, so have your registration saved to a General piston so that you can reload it instantly.
If you need an audio recording - to share with friends for instance - the above suggestions won't do that, but might be a good starting point for sorting out the problem.
I think you may be playing back via different MOTU channels than those you used while recording, which could be tricky to sort out; but try recording just the MIDI and let us know what happens.