Unfortunately that's harder than just always leaving a Raspberry Pi on at home, especially given that I want to be able to sync files to my phone, where EncFS probably doesn't work at all (or easily).
I'm unfamiliar with syncthing, but could you run two daemons, one that does encrypted sync to e.g. dropbox, and one that does plain sync to your phone and such? Or would the two instances stomp on each other or get into an infinite loop? e.g.: