R.G. Keen has a bunch of articles about switchers on GeoFex. The easiest way to do one-of-n (up to 8) switching would probably be an octal latch driving your relays. I made a switcher for my Leslie with a 74HC573, like so:

You can do the same basic thing for up to 8 switches. R.G.'s site has a good description of what's actually going on, if you need to know. The output of the 4050 (or you could use an octal buffer, but you know, I didn't have one when I did this thing) goes to drive the relay.
(Actually, these days, if you have any programing skills, you could just use a microcontroller, be it a PIC, an Arduino, or a Raspberry Pi, and then you don't have to bother with hardware debouncing - software debouncing is pretty easy...but a CMOS or TTL latch is pretty straight forward, as such things go! Don't neglect the switch debouncing!)
Pops are always going to be an issue, unless you go with a transistor switching setup. The big problem is always going to be the transitions. You can improve it a bit by slowing down the impulse which trips the relays (basically a cap across the relay coil). That gets rid of any noise from the trigger signal, but it doesn't deal with the problem of the amps loosing their ground reference so quickly, which is just going to be a problem.
You left out the biggest issue, though. While you are playing, the pops will largely be drowned out by the music. A much bigger issue is ground loops. The only safe and certain way to do it is to transformer isolate at least three of the amps. Anything else is always going to have the potential to come back and bite you - it will work in one venue, but when you get to the next it will be humming like mad. With transformer isolation, you can be sure it will be right, every night.
Gabriel