But I'm reluctant to rely on using security measures because I have had serious problems using elaborate security in FileMaker Go.
Sorry, but I think security settings within FIleMaker are the way to go, though I don't see them as "elaborate". Users from each site can be assigned different privilege sets for their accounts. The privilege set name can then be used to control which records are accessible to them.
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set this up.