How to change the default isolation level of a transaction in a stored procedure in PostgreSQL PL/pgSQL?
That should be simple:
ALTER PROCEDURE myproc
   SET default_transaction_isolation = 'repeatable read';

The downside to that is that because of the limitations of transaction management inside procedures, you can no longer COMMIT or ROLLBACK inside such a procedure.
If you need that, you could start the procedure body like this:
COMMIT;  -- otherwise you get a silly error
SET TRANSACTION ISOLATION LEVEL REPEATABLE READ;

Transaction management inside procedures is pretty limited at the moment.