We hunted with TGB Outfitting on a combo bird/big game hunt last spring. It was awesome.http://tgboutfitters.com/index.html
You can visit with them directly at the Dallas Safari Convention this January, along with several other Argentine operations. TGB took care of all the paperwork for us, but I recommend that you rent your guns ($100/day) there rather than deal with the hassle at the airports. The cost of ammo will be your biggest expense by far, and renting will save the wear and tear on your own shotguns.
You'll fly into the international airport in Buenos Aires (EZE), then you'll be escorted across the city (2-hr drive) to the local airport (DuBerry) for your flight out of Buenos Aires. At EZE we had to go through the gun check-in with RENAR (their TSA) where no one spoke English. Then at DuBerry the process was repeated again....in Spanish. Luckily, I know just enough Spanish to get by, but each step took over an hour. Then lastly, at the little airport at Santa Rosa in La Pampa our guns and papers were checked for the third time. And when it was time to return to the US, the three airports do it all again. It wouldn't hurt to plan a stay at a Buenos Aires hotel to allow for delays.
Interestingly, this month's issue of The Hunting Report has an article on gun permit costs and transit through Argentina. This article also recommends that shooters rent their guns, at least until Argentina straightens out the import process.