If I was the OP, I would consider living life a little close to the edge and having an adventure. If I was staying for three to four months at a time, go away and come back a few months later I would want my own wheels too. The car rental companies are such rip off merchants, even the big brand ones like Avis and Hertz have their own little twists with a sting at the end of rental.
I would go on the classified ads and buy a $2,000 jalopy and keep it in the original owners name. Just get a sales contract drawn up with a local lawyer. Get it insured with the minimum cover allowed by law and make sure your windscreen stickers are up-to-date. If you do ever get pulled over the only documents you need are either red or blue. The red one says 1000 and the blue one says 2000.
But in order to do that one would need a little mechanical knowledge and some tools, because it will break down. And also good command of Spanish would be essential. For me it would part of the adventure!
$30 a day for three months car rental is $2,700, so what's the risk? And if you're lucky you'll have your own wheels when you return!