DaveTheCoder I'm honestly also surprised it worked in RC4. :-)
I'm obviously doing something wrong.
I've attached a screenshot of my project structure.

The root node, as well as the "game_settings" and "input_remap" nodes have Process set to "Always".
The ViewportContainer, which contains the actual game under the "scene_manager", has Process set to "Pausable".
Every other node/scene in the tree is set to "Inherit".
The concept here is that when I open the game_settings or input_remap at any time during gameplay, the game is paused, using:
get_tree().paused = true
This works fine. The gameplay pauses, and I can still navigate the menus and buttons in the two aforementioned panels, and if I close them, the gameplay resumes as expected.
What does not work within all this, is the
_input(event)
function, which seems to get paused too. And as my remapping code relies on these events, it does not work.