You are both absolutely correct! I'm thrilled to have found this forum!
Since your replies yesterday, I've spoken to CIC. It turns out that the sponsorship application would have been rejected anyway (since she's already a de facto Canadian citizen). We've withdrawn the application (expecting a $550 refund, thank-you very much) and are now submitting an Application for a Citizenship Certificate. Because she's 1) unable to work without it (needs a SIN), and 2) in need of medical care (she's 6 months pregnant), she's eligible for URGENT processing.
Most notably, at the outset of this process I consulted 2 immigration lawyers (brief free consultations). Both of them confirmed that the only avenue was the Family Sponsorship route. They wouldn't look at it any further without a retainer. Very disappointing as it looks like it was just a money grab.
So, thank-you bigredmoose and sammystorm19! If ever you're in Ottawa, drinks are on me!
I'll follow this up with the outcome, hopefully in a matter of weeks, not months.