Lynn, I just checked rates by a few different carriers for something that size and weight and the prices are absolutely outrageous. Because of the size, the freight charges are based on dimensional weight (in this case the proportions of the package cause the cost to approximately double). And even before that penalty, the cost is extremely high, even for "economy". I've checked a few different carriers, and they range from $600-$750USD for each package (for 7-10 day transit time). I've explored shipping belongings internationally vs. bringing them on a number of occaisions, and although I did have to do it once, it was at a considerable expense over what I would have paid for excess baggage. (never THAT much more, but expensive)
I'm don't consider that practical, but if you do, let me know and I can give you the information. This price makes the added baggage fee of the airline seem like a bargain. But again, that would require that the paintings could fit into about the same volume area as a suitcase. It does vary slightly by airline, but each one does have very specific information about maximum dimensions and weights. Have you considered removing them from the frames? If you could do that, you may be able to bring the paintings and the frames more easily.
There is another option that I have used a couple of times - it's something the airlines do called "counter to counter" shipping. They don't have advertised rates for it, as far as I am aware, and the shipments that I did were quite some time ago - before 2001. Doing this now requires you to register with the Department of Homeland Security in their "Known Shipper" program (It seems that nothing is simply any more). Fortunately, the registration is a single page application and can be obtained from the airline. Here is an example of a known shipper request with Delta:http://bitli.es/miZqBz
Of the options you have to ship to Cancun, it appears that traveling with the items may be the most cost effective, even with the extra charge. If you have any questions, just let me know.