Reminds me of someone who proposed a similar scenario to an ancient sea captain in the Age of Sail. His answer: I would not have allowed the situation to get that bad.
Agreed! But, assuming you'd got yourself in to that Godforsaken place...
Go-around (you should have enough fuel for the full procedural missed approach - the skipper could modify the published if needs be to reduce burn) and put in as much prep/thought as you can until it becomes critical to start the approach (fuel-wise)?
Running the checks may well get the flaps/slats moving to where they should be, allowing a normal config for the approach.