When I did mine (almost 25 years ago, so take that for what it's worth) that was the one part of the program Purdue did under Part 141. As I recall, it was 9 hours of instruction plus one for the check ride, so Tony's estimate sounds about right.

I'm also confused about the "Commercial Instructor Certificate." Not sure what that is - I've been out of the CFI business for quite a while now, but I thought the basic flavors of CFI were:
CFI-A Airplane
CFI-I Instrument Instructor, and
CFI-ME Multi-engine
It's certainly possible something has changed along the way since I went down that road, but from what I'm reading the only things I see you needing are the ME rating and ME Instructor if you wanted to add that.

I do think your revised plan is a lot better, particularly since you'll be able to gain experience instructing during the two years you're working on your BS degree.