On the Nexus 7 there's not a separate menu option for "Reboot into safe mode". You have to long press on "Power off" and then the safe mode dialog appears. I'd try that, since I imagine it would work the same way if the GNex supports it.
Looking through the Hyperdrive ROM page for Note 3 at XDA, power menu toggle can be adjusted by the following steps.
Open the application Hyperdrive Tweaks included in the ROM.
In the app goto General Mods > Extended Power Menu
Select the options you want for power menu toggles viz (Shut Down /
Restart / Recovery etc).
However, I cannot find out where ...
Disabling the power button and changing the volume_up button to power did end up working (i.e., prevents faulty restarts at random times.) I also verified that long pressing the actual power button does end up restarting the device, which means that restart is somehow programmed at the hardware level.
I discovered the answer literally 1 minute after asking the question so I thought I'd answer it myself in case it's of any advantage to anyone else.
There's a very simple ( but quite odd in my opinion ) solution to this. Simply adding the clock app to the the shortcut screen of Max Power Saving Mode ( by clicking one of the plus signs ) solves the issue ...
Some OEM ROMs offer such a functionality, most do not. You can check your device's settings, if there is such an entry. If there is none, then it is not possible. So, the answer to this question will be a yes and no together. It will depend on which smartphone you have.
You can certainly not achieve this with 3rd party apps.
This feature is in Cerberus Anti Theft and also in some custom android Roms (Such as Exodous). It doesn't require root but like any anti-theft software there is a paid version as the free one is limited to 30 days.
But you could try the Smart Screen Protector App which is also mentioned in one of the other answers.