I would reach for my handheld GPS and handheld radio and sort myself out with a DIY GPS descent somewhere, or get help from a radar unit if you can find one.
That's the obvious answer.
In your scenario, Fuji, I can't see there are any options if non-radio, and if you have a radio then you would get a radar letdown somewhere.
If truly out of options, all one can do is set up a minimum descent rate and descend, very slowly, and hope for the best.
Not sure how the localiser approach is relevant if you don't have anything with which to receive it.
In the UK, you will never be far from the sea so a timed leg offshore would be worth trying.