Not going to get into the debate about FDs and APs, but it is worth noting for those who might encounter same issue this in the future-

If you have a Stab/Mach trim failure that won't reengage, push and hold the red AP Disconnect Button for 20-30 seconds, then try to reconnect the trim. In my own personal experience (both in the CRJ and the Citation), this simple act will clear 99% of the issues that aren't related to "EFIS COMP MON" type things. (Think of it like a "CTL-ALT-DEL" for the trim system). Don't know why they don't include this procedure in the QRH...

Sounds like you guys did a good job though!