I used an expired registration for many months all over Latin America.....until someone finally noticed. When they do notice--which is only a matter of time--it's sure nice to have the current registration in reserve.
The same thing has happened to me while traveling in Europe using a high-quality, two-sided color photocopy of my registration. No one noticed for many, many months....until I got to the Ukraine, where the border guy hardly even glanced at it before dismissing it as a photocopy and demanding the real thing. Again, it was nice to have the genuine registration to offer.
Cross enough borders and stop at enough police roadblocks and sooner or later you'll run into someone who knows ersatz from genuine or reads English well enough to figure out when something expired last month. Don't get lazy about these things. When you're called on it, you really want to be able to apologize and offer the real document.
I'm not clear whether the OP understands that his insurance is not going to be valid once he enters Mexico. At that point, it no longer matters what your B.C. insurance policy says.
Hope that helps.