From what DOMCT203 is saying, 4 switches per amp will mean the gcx will be reserved for nothing but channel switching.
I did not say 4 switches per amp for channel switching, it is 4 switches total, and for strictly
channel switching it could be done with a Control Switcher or GCX. Both amps default to channel 1, and only have 1/4" switching jacks for ch's 2 & 3. If the OP only wishes to change channels on both amps and chooses to use a GCX, he will still have 4 free loops for either more function switching or to use with pedals/effects. The OP only asked about "Equipment needed for channel switching two amps at once", and with that the Control Switcher would work, and be less of an initial $$$ cost.
That being said, the gcx is a switcher, not a controller. You will still need to use a GCP or compatible midi controller to program all of this stuff into the gcx and midimate.
The OP has already stated he has a MIDImate.
Exactly what features do you need to be switchable on each mesa head? ch1, ch2, 3, solo, eq, mute....?
Very good question indeed, and the answer will determine how many switching relays are needed.
If the OP doesn't currently use a rack based setup, I would use the Control Switcher(s). They can be placed on top of the amp head(s) when in use, and put in a gig bag when done. If the OP deciedes he wants to control more than channel switching, he can use one Control Switcher per amp head.