Thanks for the detailed replies - I appreciate you sharing you knowledge, Rewolf! I'll tell you what I've found so far, and what I've done to be able to control everything satisfactorily.
First, I found the least offensive amp for keyboard (piano, suitcase, wurlitzer, organ) reproduction seems to be the Class-A 30 model, with the DT25 set to Triode (rather than the default pentode) mode. There is very little hiss/noise, I've dialed out distortion and fuzz I was getting with the blackface models, and I've thrown in a noise gate, turned down to 10% for silencing it when I'm not playing. Also, I set this patch to only take the Guitar In, which I've plugged my keyboard into.
Likewise, I usually keep all patches at Guitar + Variax inputs, but I've taken the patches I'm using at this gig for just Variax, so I don't have to turn down the keyboard when I switch to guitar.
Finally, I did replace the crapola Casio keyboard I was using as a simple MIDI controller with a new Novation Launchkey 61, which has a ton of adjustable faders, dials, and pads. I am controlling the laptop's output volume in Mainstage from the keyboard itself now, and it's working well.
I may venture into the deeper MIDI editing you have introduced me to as I use this rig for more gigs. Thanks again!