OP kscott: It’s strange you have no vacuum line to the front motor mount. I checked rockauto and the mount showed a vacuum connection for 2002. By front, I mean behind the radiator, down low, middle of the MDX right/left. Yours’ might route differently but on a 2006, there should be a tube going from the engine and then a hose from the front of the engine crossing the gap between the eng and rad - then either a tube or hose going down between the rad fans to the mount. If it’s a tube between the fans, there should be a short hose connecting to the mount. Maybe yours routes differently and you’ll need to get under the engine and look for the mount and hose.
If it starts right up and doesn’t hesitate when accelerating (like onto a freeway) your fuel pump might be / probably is fine.
The valve adjustment can be tricky and if not done right, could result in misfire. If you had a competent shop do it or you’re confident it was done right, then probably not the cause.
There is a fuel pump relay and a separate ignition relay. Not sure if those could be intermittent or going bad. There’re fairly inexpensive on rockauto, expensive in brick auto parts stores.
If the TB ever broke, you could have bent valves. If ever overheated, a leaking head gasket. I suppose if the belt were really old, the timing could be off or varying. Keep in mind, it’s 105K miles or 7 yrs for changing. You definitely don’t want it to break.
Good luck!