You would need to check with your insurance carrier to confirm that
liability insurance is provided in Mexico (not just collision insurance). National in Mexico requires that you have TPL that is specifically valid in Mexico:
The purchase of Third Party Liability (TPL) Protection will be required at the counter unless you show proof of coverage. Most auto insurance policies from outside Mexico do not provide coverage in Mexico. Liability insurance purchased on third party travel websites and credit card policies are not accepted.
The detailed terms and conditions state:
In Mexico, Third Party Liability insurance is required by law on all vehicles. Customers can obtain coverage for damages and injuries to third parties, up to the policy limits, under the local rental car company's insurance by purchasing its Third Party Liability Protection (TPL). The purchase of TPL is required unless the customer presents valid proof of current liability insurance specifying coverage in Mexico.
Please be aware that most auto insurance policies from outside Mexico do not provide coverage in Mexico. Liability insurance purchased on third party travel websites and insurance that accompanies US credit or debit cards are not acceptable forms of coverage. Employees of the local rental car company are not qualified to evaluate the adequacy of the customer's personal auto insurance coverage. The customer should contact their insurance company in advance of the pickup date for the rental with any questions regarding their specific coverage. Further, if the customer provides acceptable proof of current liability coverage in Mexico and declines to purchase the TPL offered by the local rental car company, an additional authorization in the amount of $2,500.00 USD will be held on his or her credit card.
In our experience, it will be difficult to avoid this even if you have a letter from your insurance carrier attesting that said policy for liability is valid in Mexico. That's the scam down there--super low base rates and then mandatory liability insurance so they can make a profit on the rental.
Additionally:
Customer must purchase an extension of liability protection to cross the border into the U.S. at $10 USD per day - this amount provides TPL up to $100,000 USD, PAI for the passengers up to $2,000 USD per person and up to $10,000 USD per accident.
As far as swapping cars, don't bet on it. The car is going to have Mexico plates and it's going to be a huge pain for any U.S. location to get it back to Mexico. I'd be shocked if any U.S. locations were willing to swap it unless under duress, and even then, they may just tell you NO.
In short, while your approach is creative, it's not likely to be cost-effective when all is said and done. You're likely going to end up paying more and possibly creating a huge hassle for yourself if something goes wrong.