Hey Buster...
The MESA PRO (HGAS) HIGH GAIN AMP SWITCHER only switches preamps...
You would feed all of your Heads FX sends, (or Slave outputs if your amp has them) to the HGAS, allowing you to switch and combine any of those preamps to a single return that you would send to your Time-based FX and then back to one of the head's FX Returns using that one Head's Power Amp Stage or a separate rack-power amp as shown.
Again, with the above set-up, unless your heads have Slave-out as shown above, and since you are not using the FX returns of the other heads, those heads will have to have load boxes on the speaker outs so that you do not fry your Heads.
The other complication is that the MESA HGAS requires contact closures from a control switcher to operate...which is another piece of equipment that becomes another single point of failure therefore reducing your reliability.
The easier way to switch those heads is how you mentioned... by using something like the Radial that switches speaker out's... But you need a 3 input one that will switch 3 Amp speaker outs to one cabinet....and I have never seen,
or don't remember,
one like that.
So you will need to track down one of the other 3 or 4 output amp switchers that will switch your guitar to 3 or 4 amplifier inputs... (in that case, you will require a cabinet for each amp)
Here's a few that switch the guitar to 3 or 4 amplifier inputs and transformer isolates the amps to eliminate hum problems...(very important!)
http://www.frampton.com/3banger.html
http://lehle.com/EN/Lehle-1at3-SGoS
http://voodoolab.com/ampselector.htm
PS: using the above complicates FX insertion unless you are using some type of control switcher (Voodoo Lab GCX or RJM Effects Gizmo) to switch the FX in conjunction with the Amplifier Switch.
I hope this helps!
seeya
Joe