Could the MX2 controller be wired to the buttons of a Canon remote IR trigger to provide wireless operation?

Yes. You've established that you have a button. That button serves the following purpose: to connect two wires or close a circuit

The MX2 essentially does the same thing to trigger a camera: close a circuit

So, the two wires leading to the button would need to be connected to the two wires that correspond to the trigger circuit coming off the MX2! That's the TIP of the 3/32 TRS pin and the last ring (not the middle, that's for focus). Someone correct me if I'm getting the poles wrong here...

I have tried using the Canon wireless remotes hooked up to timers on a couple of different cameras, but found I was dropping frames quite often.
Also used them for triggering two cameras for 3D shots.
In the end I concluded it was just not reliable enough, so always use a hard wired option now.

Could it be a case of timing between the half and full press needs to be tweaked with?
I'm guessing a few variables such as remote battery freshness, camera mode (wake on half press), lens setting (AF/MF), frame interval etc may have an affect? ...the IR depends on line of sight as well. It's something I would still like to play with, to reduce cabling if nothing else.