Crypto-Atheists

The idea scares the hell out of me: namely, that
one of the people in my congregation is an Atheist
masquerading as a Christian for social advantage
(or sexual advantage, for that matter).

Is there some tried and tested method that allows me
to determine whether or not a person is a true believer?

You can't easily test for atheism, but you can test for instances of christianity.

Protestant will clench their fists and teeth when looking at a catholic.
An adult male catholic will get visibly agitated when looking at a little boy.
A catholic boy will clench his anus when looking at a catholic man.
An eastern catholic (orthodox) will, in addition to traits displayed by western catholic, seek out drugs and abortion to condemn and indulge in.
Other variants will inform you of their faith themselves, even before nearby vegans manage to announce their dietary preferences.

If your specimen doesn't display any of the above traits, they're either a woman or not a christian.
In the former case, you shouldn't trust them regardless of all other factors.