"A commenter mentioned using Dropbox for synchronization as well, which seems attractive, but I’m not sure how clean that would be on headless Linux servers." Dropbox does work pretty nicely on headless Linux servers, you just have a daemon running constantly with none of the GUI extensions. I use it for keeping some code in check.
Nice list of things to try, I don't use vim but I've been putting off doing 3 of them (caps remap, iTerm and zsh).