Can you tell us when you graduated? And when did your study permit expire? I just don't see how they would have renewed an off-campus/co-op work permit without your having a valid study permit.
See, the worst part of this is, technically, since graduation (or 90 days after graduation), it sounds like you have been living and working in Canada without authorization. CIC not only has the right to refuse your CEC application, but based on what you've told us, they could deport you. I doubt that will happen so I don't mean to stress you out, just think you should be aware of all the implications.
I would like to think that CIC could see this as an error of technicality rather than intent, and there would be some scope to make amends and correct the error, but I really don't know how you would go about that - this is one of the few circumstances I would actually I would suggest you see an immigration lawyer... unfortunately it sounds like the lawyer you do have is not a specialist in immigration law. Perhaps your lawyer knows someone...
And no, I've never seen anyone talk about this problem in this forum, but I'm sure it's happened.
Immigration gave me a work permit that expires years after my graduation. But thanks for your thoughts and input!