Regarding the MIDI side of this, there are probably a few ways to solve this and it will depend on the functionality of the Adrenalinn III and exactly how you want it to work.
You mention that the Adrenalinn III can not do MIDI THU and OUT at the same time.
If you can set MIDI Tap Tempo from the MIDIMATE to the Adrenalinn III ok and it can send out MIDI clock then you could use a MIDI splitter after the MIDIMATE and feed one cable to the Adrenalinn III and the other to the a MIDI Merge box.
Then go out of the Adrenalinn III into the other port on the MIDI Merge box, then out of the MIDI Merge box into the first Factor box.
This would allow you to add the MIDI clock to the MIDI chain.
Another option might be if the Adrenalinn III supports MIDI maps for out, then you might be able to do something there too.