There's a relay, Rhy1, which is switched on for R2/Lead but is off when R1 is enganged, it's purpose is to drop the level of signal going to the poweramp. Beside this relay, the rest of the switching in the MarkIV circuits are performed with noiseless LDRs, and it appears that Mesa used a relay here to save the expense in using 2 separate LDRs, along with transistors and rest of components required to switch them. The solution or a potential mod is to use a small circuit to replace the relay with 2 LDRs.
Logically, using the footswitch or the amp to switch channels is electronically identical (the footswitch turns on the same parts of the switching circuit that the pulls do) so pops will occur either way.
I'd be interested to know Mesa has to say on this.