Daml tuples are translated into records with fields _1, …, _n. Navigator uses the JSON encoding used in the JSON API, so you should end up with a JSON object with those fields. For Set, take a look at REST JSON Specification - #4 by Gary_Verhaegen.
That said, I would recommend against using the custom frontend config in Navigator. It is very limited and we have no plans to extend it. If you need a custom frontend you are better off building something using the Javascript bindings. create-daml-app
is often a good starting point.