I just tried, four possibilities:

1) Assign either your Monitors or Phones to "Main Out" in the different snapshots
2) Change TM FX settings manually on demand
    Options->Arc & Key command settings->ARC USB Settings->Default Encoder Function: Main Out (Default), Phones 1..4, ..

These ARC USB settings seem to be part of workspace settings.
I validated it by
a) selecting a different snapshot, changed the "Default Encoder Function" from "Main Out" to "Phones 1" and changed back
    Result: "Phones 1" is still selected, selecting the other Snapshot didn't change it
b) Pressed ALT-1 (Quick Workspace Select of Slot 1), this restores the whole settings (Snapshot and Workplace settings)
    Result: "Default Encoder Function" was properly restored to be "Main Out"

Based on this observation I see two further possibilites
3. Save two different workplace settings, one with "Default Encoder Function" to "Main Out", another to "Phones 1"
4. Once you have finalized your TM FX setup in terms of Snapshots/Routings
    save all your settings in two different Quick Workspace Select Slots 1 and 2
    TM FX winows needs to be open and active
    Then you can restore with one keypress "ALT-1" or "ALT-2" either Quick Workspace Select Slot 1 or 2
    with the different settings for "Default Encoder Function" to "Main Out" or to "Phones 1"

All has its pro and cons in terms of operability. I think the best useability has Option #4, but you need at least to open your TM FX window as prerequisite for it to work, which is maybe also a bit combersome in terms of easy operation.

@RME: I am not sure at the moment whether its possible or whether this might have unwanted side effects.

But wouldn't it be maybe a better solution to think about storing the value of "Default Encoder Function" in snapshots instead of workspaces ? Then you would only need to select your Snapshot and could directly control the volume of either Monitors or Phones.

EDIT: would also be a nice solution to store this in snapshots, because then its also very easy to be used in standalone mode when connecting the ARC USB to the UFX II or UFX+.