How to quickly adapt your patch from using an amp to using a PA?

Hi! So I’m new in this digital world and I sold all my single pedals just to use the tone master pro and some extra distorsion pedals just in case (metal zone and abasí pathos pedal).

So my setup is using the tmp with a fender dsp mustang ms4 4x12 amp which sounds really great specially disabling the head preamp. And these setup I connect it to my computer which works and sounds great. But I want to be able to easily move from home to a friends house to record other guitars with some friends and just move with my guitar, tmp and a headrush FRFR 108 which is really small but the same patch hears horrible and over saturated even though I have a head and cabinets on my preset.

The patch I must use is the one from the picture. Can someone help me? I tried lowering the master output when using the PA, changing order of the fxs, head and cab but nothing seems to work.