Actually, I've not come across that particular conflation-with-overlap before in this context. Have I been out of the NYT Sunday Puzzles loop for too long, or did you just devise it? :-)

baring + ingest, for example, with appropriate cluing-->baringest ===> BAREST

No, I guess that's discarding the overlap. Not the same thing.

Here's one:

Sign in the undergratuate physics lab:
"IN THIS LABORATORY
USE MORE OF THE FIRST FIVE LETTERS
AND LESS OF THE LAST SEVEN!"