Put only a backup copy (not the source file) into Dropbox or Tarsnap. Don't delete the file on either system. Same boat. Scripts can copy out from the Dropbox

Put only a backup copy (not the source file) into Dropbox or Tarsnap. Don't delete the file on either system. Same boat. Scripts can copy out from the Dropbox to both negate your issue and proliferate backup copies to many physical locations.