A couple of thoughts cross my mind upon reading your response.
I thought you might be investigating the limits of Whiz Deletion, so that didn't surprise me. I tried a similar analysis.
I thought, what about thinking of the
-ing as a substitute for the infinitive
simultaneous with the Whiz Deletion:
She found a position, which was to teach English ...
That is, the only reason the Whiz Deletion seems wrong is that the
"which was" sounds a little less elegant with "teaching" than it does
with "to teach".
Nonetheless, one might accept
... a position, which was teaching English ..., don't you think?
Have you read Hela's question on
writing a letter professing his love?
Does that appear to be similar to the kind of thing you're
investigating? Could it be another example of this same
phenomenon?
Lastly, I'm not sure I accept the concept of an ungrammatical idiomatic
construct!
![Smile [:)]](/emoticons/emotion-1.gif)
If everyone says it and not a linguist in
the land questions it, it must be grammatical, no?
CJ