> 'Save the webpage as I see it in my browser' remains a surprisingly annoying and fiddly problem

You may be interested in SingleFile[1]

[1] https://github.com/gildas-lormeau/SingleFile

I use it all the time to archive webpages, and I imagine it wouldn't be hard to throw together a script to use FireFox's headless mode in combination with SingleFile to selfhost a clone of the wayback machine.