I no longer have the English grammar books I had back then. Even if I did, I suspect they might not have finer points like the one you mentioned, as they were for grade school kids. I actually went to a web site I tend to frequent these days for my english students, englishclub.com and... I finally found its section on prepositional phrases -.- It was hidden in a page on phrases in general:
Anywa, I figure if I make the mistake as a native English speaker that's read a lot of books and written a fair amount, and that sites meant to help English teachers don't cover, it's probably not that big a deal. I can't see myself saying "at which I started", but I certainly could have said "being a native English speaker was enough to get a pass to do hired in the first school I taught in".