I pay them using Transferwise, it works like charm. They use a local bank (BBVA, I think) for the actual payment to the consorcio, so the consorcio doesn't even know I am paying from abroad. It costs just 1-2 dollars (it depends on the transferred amount).
I was just reading that there have been a lot of new changes and recent restrictions to the transfer of foreign currency in general, including into banks. I assume that what you suggest is doable RIGHT NOW? If so, I will look into it. I like what you said about "working like a charm".