As someone who has been teaching for over a year and a half in Mendoza, I have found that in my experience the comments are valid here as well, except that often the wages are even a bit lower here.
This is the big hiring time now (the silly season, as there are all kinds of games that desperate directors play until they settle on the right teacher for the right course, their word is usually worthless), the classes are starting or starting over the next week. The other secndary time for hiring is in late July and early August after the short winter break. Usually, the language institutes are only interested in Argentinian teachers for contracts , and prefer to hire Foriegn native teachers for individual course, such as advanced regular or conversation, or for private individuals who feel they want a native teacher.
The big battle I always have to fight as a gringo applying for a course is that we gringo teachers as perceived as difficult, only going to be here for a while (even if we tell them we are permanaent residents or here for a determined period), untrained (even if we show them our credentials), poor at teaching grammar (there is some basis for this, as we are not taught grammar as a subject generally in anglo schools), and that we do not correct pronunciation (largely a myth). Thus we have to fight many myths and prejudices, and this is a credibility game we have to play on our part. Have any refernce letters and qualifications copìed and hand them over, as Argentinians are children who live in the present. Do not expect them to telephone you back as promised, you have to follow-up to a greater degree than would appear reasonable. NEVER expect a reply on email, as email etiquette does not exist in Argenitna.
Many Argentinian English teachers are good, but few have good accents or can teach pronunciation well. How many, for instance, pronounce "would" as "good"...probably close to 95%. also, Argentine teachers often make up definitions for idiomatic or specialized vocabulary. So, there are sometimes valid reasons for students asking for native teachers, even if the locals are grudging about this.
As a strategy, I am trying to work for more sensitve (and sometimes smaller) institutions, and to develop a small group of clients of respecting , respectable and reliable students, who can pay me directly, which avoids all kinds of complications. The trouble is that you will get burned often as part of the process.
Good luck. You have to be very careful, flexible, patient and have a good sense of humour.