OK, to respond to the OP, it seems that it CAN be done, sort of, but it would require a MIDI controller and you'd still have to program each individual rig combination.
You could use a separate performance page for each FX preset, with the 5 rig slots used for the different amps/profiles/gains.
Ex:, Slot 1 as JC-120 Clean, Slot 2 as Fender Super Reverb slight breakup, Slot 3 as a dimed Plexi, Slot 4 Bogner XTC Blue, Slot 5 XTC Red. Copy these 5 plain profiles with no FX across all performance pages.
Next, build your FX presets. Put them in all 5 of the rig slots for a given performance page.
Now, set "Performance Load" to "Keep Slot".
In this config Selecting the slot with CC50-54 changes your amp but leaves the FX. Selecting the Performance Page with CC47 changes the FX but keeps the amp (same slot).
You still have to build them all, but having a no-FX performance page template and FX presets makes it fairly easy to do. 128 performance pages covers a lot of ground.
yeah...it’s possible indeed, but there’s to much complications to my taste.
Managing so many presets, current state of expression controllers, a quick tweak of your amp sound takes adjusting a dozen rigs....to complicated!
I hope they consider my suggestion....and be the first in the market to support oldschool methods in a unit of today