Thanks for the clarification, but giving up performance is a no-go for us.
Also I have my concerns about shemaqualifying each and every use of the -> operator, there are really a lot of them in my functions and it would severely impact readability.
Are these the only 2 solutions possible?
At present, yes. The system tooling enforces a nearly search_path-less execution environment (you basically only get pg_catalog and pg_temp). The only other possible solution is to somehow get the extension installed into pg_catalog.
This is basically a security trade-off since the goal is to avoid having the insecure public schema in the search_path. I'm sure that if we tried we could come up with and implement one or more ideas to make situations like this less painful (e.g., allow a DBA to mark a schema as privileged and then it gets added alongside the pg_catalog schema). Some options may not be as simple as adding a new command line option to pg_dump/pg_restore to enforce a custom search_path, even one that includes public, thus giving some measure of control to the DBA. We still haven't done that (though I suppose if we solved this problem in a more systematic way the need for such a pg_dump option very well might go away, it's basically the same problem).