Thanks for your replies, folks! Following up on this, I spoke with a number of educated folks, and I can report the following:
* Active Texas insurance is absolutely required to renew registration... being insured in Mexico isn't enough! I even read the law: https://statutes.capitol.texas.gov/Docs/TN/htm/TN.601.htm#601.072
* I ended up purchasing a new minimum RV policy from Progressive for ~$225/year, using that to renew the registration, and cancelling it after a month, so only paying about $35 total.
That's the best option I could come with! Hope it helps others!
With regards to the question of running afoul of any Mexican requirements to register the vehicle there, that's a really great question, and I'll need to look into that now.