It's too late to help your son, but I will post a reply in case anyone else is interested. Folks from the US can/should get a 10-year visa. That does NOT mean you can stay ten years. It's a prerequisite to temporary residency. However, if you have it, you can temporarily exit Paraguay by bus, visit Argentina, and re-enter. After I did that for about 14 months, I started getting pushback at the border but was able to get in anyway. Shortly after, my residency application was accepted, so I have had to leave since.