Not sure if this is too late for many of you folk but after much the same frustration I came across this today…
https://www.wordimpressed.com/plugins/how-to-use-wordpress-jetpack-for-local-development/
I haven’t needed to test all the modules but it does work on two or three I do need.
That said I’m having trouble serving up images to my ‘Tiled Gallery’ module…
perhaps something to do with the required ‘extra-special processing’ ?