Is there a process or paradigm for analysing the game theory of this and other kinds of changes to Bitcoin?
Yes, twitter threads :P
Seriously though, forums like stacker news and bitcoin twitter and podcasts are where this stuff typically gets hashed out. Experts in the subject matter are brought on to give their opinions and node operators listen in, sometimes ask questions, and ultimately decide whether or not to install the soft fork software on their nodes. It's how it's been done since the OP_P2SH softfork in the days when everyone hung out on bitcoin talk forums. Now we're spread around further and there are node operators all over the world, so the number of forums is bigger, but it's basically the same process. Bring in experts, ask them questions, make informed decisions. And sometimes sell hats to drum up support for your "side."