it seems to me that the placement of the tongue is "attached" to the sound that follows (th or s), not to the n sound. Or is it not possible to isolate the n sound from the surrounding letters?

Bingo! Nancy you've hit the nail on the head. It is, indeed, impossible to isolate the nasal sound from the surrounding letters, hence from the particular position of the tongue. Whilst the practice is not common inEnglish, in languages like Hindi, people learn to pronounce, and distinguish between, all these 'n' sounds. Nobody from India would mistake the anther n (even when pronounced separately), from the under n. And so on.

cheer

the sunshine warrior