Power-On Modes (Press following button combinations while powering on Montage 6/7/8):

[UTILITY] + Part [COMMON] = Touchscreen calibration. Closely follows Owner's Manual pg 46 shortcut except requires no [ENTER] during poweron
[UTILITY] + Cursor UP = Apparently forces a firmware update attempt (if no USB flash drive installed, will show "Searching for update ..." and gets stuck. If there is a flash drive installed and no update file, eventually will show "Searching for update ... NG" and ask to retry.

That's all I've found thus far -- leaving it up to the community to find more.

Other undocumented features:

1) Connect a keyboard to Montage

Keyboard (tested a low-grade "Inland" brand wireless keyboard) works. In "Live Set" view, the arrow keys and "+"/"-" keys are active. One idea for a "hack" which goes beyond the assignable momentary footswitch for advance would be to use a WIRED keyboard (less to go wrong) and make a footswitch with the "+" and "-" keys wired to rugged momentary switches. This would allow to advance to next ("+") and previous ("-") performance in a Live Set at very little cost.
More on keyboard - in Performance mode, the arrow keys scroll around. Pressing Enter on the numeric pad of the USB keyboard will select the item. Pressing "Esc" will place the UI "in the weeds" requiring using the touchscreen to get the UI back on track with respect to the USB keyboard. If you stick with "+", "-" and "Enter" (numeric pad) to change values and to continue, the keyboard can be used exclusively. Lack of proper support for "Esc" makes cancel with USB keyboard problematic. I have not found a work-around. Note that "Esc" is sometimes supported such as in the "Name search" for selecting a patch. The numeric values (such as common assign) have issues with cancel&USB keyboard.

Note that when changing performances, there is a delay. At 90bpm playing triplets if I change programs on the downbeat, the sound will change on the 3rd note of the triplet. This also matches the behavior if I change performances by using the touchscreen so there is nothing unique to the keyboard in terms of the delayed reaction time. I have not compared with the footswitch. It would be nice to have a lower latency in performance switching.

2) Connect a larger video screen to Montage

USB device to video works. Yamaha is going to document how they do demos showing the touchscreen output on an external USB-to-?(video)-connected screen. At least one user has tried a Startech USB to DVI adapter (credit: Stephan) which seems to work with minor flaws. Wait for Yamaha's official supported list for a more "perfect" solution. Unless I'm mixing experiences up, this adapter produces a green bar at the bottom of the screen. Given the demo here ( https://www.youtube.com/0614baa4-4fc1-4183-bb2b-b2ad0afed45d) also shows a green bar - chances are you're fine using the StarTech solution

3) ... "and more" (for the community to add.

There are other observations which are not undocumented features but more of "bugs" which may be fixed in later versions of firmware. Other than limitations of the features - I'll leave the bugs out of this list.