That being said, the thing I'm most interested in here is how to integrate Memfault with my codebase, and that's the only thing I can't figure out! Your docs pages are quite pretty, but don't include the interesting bits! Clicking thought into the demo doesn't really help.
Any chance you'd consider publishing that to the site?
You can find some of the more interesting bits at https://github.com/memfault/memfault-firmware-sdk, which is our public facing firmware SDK. This gives a rough idea at the steps necessary to implement the coredump features of Memfault.
(Before digging into the SDK to see if this exists), is there any chance you'd support some form of "custom transport"? In the system I'm working on the micro is only connected to the network via a single board computer through which I'd need to shim the Memfault connection.