Though this answer may not help much, I chime in, because I do know of a solution...
In practice, it's never come up, which is part of why I toss this in...
Interestingly, there is an amp in the wild, that covers your particular situation...
In the mid 80's, Peavey added to their lineup, the Stereo Chorus 400, available both in head form, or 212 Combo, (see included combo image)... Now only available in the used market, they are out there, reasonably priced...
Their top of the line Chorus amp, it's the only true stereo amp on the market, that I'm aware of... 130 watts per channel, 260 watts in stereo configuration... It's truly 2 separate amps in one. In normal mode, functions like most Stereo Chorus amps, plugged into channel 1, your signal is controlled through preamp 1,sent in stereo, through power amp 1, & 2... The footswitch includes the option to split it up, morphing into 2 entirely independent amps, in one cab. Identical Twins, essentially. Guitar 1 through Channel 1, Guitar 2 through channel 2 ...
As you may imagine, this provides the ultimate solution, for what you want to do... I'd highly recommend you hunt one up, not only as a quite unique solution to your issue, but also because it's an awesome amp...
I wish I could say I have one, therefore have first-hand knowledge of it... Sadly no, but it tops my Gear to find list, (Nearly acquired an SC400 twice, fell through both times)... I do, however, have its little brother, a 160 watt '94 Classic Chorus 212, which has served as the core component of my gig rig since '06... I've used Peavey amps & PA gear since '82, in every band I've been a member of. I do all my own repairs, as well, and know them inside out...
The main reason I answered, while doable, In my opinion, running two guitars, simultaneously, through a mono amp, won't be all that great, sound-wise, unless both are playing exactly the same thing... The SC 400 is the only amp I know of, that actually can do so, without adverse effects, such as both signals walking all over each other... Given it is literally two amps, each feeding a speaker, crosstalk is eliminated entirely...
