No carnet needed for Ecuador
I entered Ecuador last month. No carnet needed. There were a couple of Germans ahead of me who insisted that the customs officer look at their carnets ('We paid 10k Euros for these and we are going to use them). It probably took them 10 minutes less in terms of getting the paperwork done, but I had absolutely no problem. The carnet requirement was done away with about 3 or 4 years ago. If you do a search you can find the exact citation for the legislation. I carried a copy of the notice saying no carnet needed just in case, but didn't have to use it.
Panama City, Panama