Summary: FM-X default "Init" performance ([CATEGORY SEARCH], "Init", "Init Normal (FM-X) ) produces the sine wave. (There are other options from AWM2 as the sound source). Use the "routing" (Part Common: "Effect" -> "Routing") to select the part output as Assign L ("AsgnL") instead of Main L&R. This will be your mono output (the assign L balanced connector on the rear of your Montage). Same routing screen you can turn RevSend to 0.

It, this assign L output, is not affected by the master volume control.

You were not specific on the sine wave properties (frequency/duration/triggering/etc) so I'll leave that to you.

it will not let me change the routing on the Use the "routing" (Part Common: "Effect" -> "Routing

The only way I could see you "go wrong" vs the instructions I gave is to select the performance global routing - which would be fine since this is a single part performance - there's not much of a distinction here. For me, both the performance-level routing and part-level routing allow me to change the touchscreen area where the output is selected.

I understand you're saying the results are different on your end, but let me go 1-2-3 with this to see we're on the same page process-wise

Edit: assumes already starting with an initialized performance - let me add those steps:

i) Press [PERFORMANCE] (HOME) button (may be redundant, but my usual "get Montage to a known state" instruction
ii) Press [CATEGORY SEARCH] button
iii) Touchscreen (TS): Near the top you'll notice darker grey "main" and "sub" categories to select from. On the far-right of the collection of these touchscreen boxes are two buttons with more separation than the others "No Assign" and "Init". Press the "Init" button. In response you should see a new list of options under these boxes which are the various initialization performances
iv) TS: Touch the "Init Normal (FM-X)" performance which will hilight it with a white box around it
v) Press the [ENTER] physical button on the keyboard (located under the DATA DIAL aka "jog wheel" in the lower-right of this group of buttons)

End of edit ... continue for rest

1) press [PERFORMANCE] (HOME) button
2) Touchscreen (TS): Touch the name which is directly above the square "Arp Off". Should say "1" on the first line "Init Normal" on the 2nd line "(FM-X)" on the 3rd line. I go to this detail since at the top of the screen the entire performance has the same name and clicking on that will lead you to performance-level options vs. part-level. For the instructions, I was intending part-level although either are OK as discussed above.
3) TS: left-hand popup displays, select/touch "Edit"
4) TS: lower-left, touch the "common" square. This will highlight it a blue/green color.
5) TS: left-hand menu bar - touch "Effect" -> "Routing"
6) TS: within the lower-right of the grey background area is a box that should read "Part Output" on the first line and "Main L&R" on the second line. Touch that box. You should see, in response, a popup menu appear in the far-left of the screen. The menu is white at the top (selected item = Main L&R) and light grey for the various other options.
7) TS: Touch "AsgnL" which should be the 4th option down

That helped immensely! Thank you so much

Glad I could help.

... pivoting to use this as a motivator for some form of central repository for user generated performances:

If this is a normal type of setting for using a talkbox - and other keyboards have some preset that automatically has configured a performance (or whatever term they call it) to make external talkbox usage "plug and play" - then it may be worthwhile for someone to host probably an X7B/X7U/X7L (save file) of a user performance which sets this up. SoundMondo would be a nifty place for such a thing if/when that comes online - but in the interim there are a few places where user performances can be archived/indexed.

Then for some of the "standard fare" type setups - one could say - 'check with "xyz site" first for what you're looking for then check back if you did not find anything or what to learn about the steps necessary to build such a performance from the ground up'.