I talked to Caza y Safaris a couple of years ago when I was looking at a red stag/buffalo hunt. Went with another outfitter down there, though.
As far as other species to shoot when you are down there, I would want to shoot a capybara, white lipped peccary, and a brocket deer (the native species that you can't get in NA). I am not sure how those species are handled - pretty sure you still can not export native animals out of Argentina. You should check on that and make sure they are priced reasonably if you can not export them.
I had a nightmare trying to get my stag out of Argentina and finally gave up after almost 2 years - and I could speak to the export agent in Spanish. Many promises and no results. When they finally told me what I would have to pay just to get the cape and antlers shipped out (more than the cost of the hunt!) I told them to keep it. I was not pleased at all with the way that went. Make sure you have all your export requirements understood. Have heard a lot of hunters have significant problems getting trophies out of that country (or not at all). For all the hunting industry in Argentina, you would think that they could figure out the export issues.
When I told them to ship everything but the capybara, along with a stern email to my outfitter about his reputation, the remainder of the shipment was sent after two years. I have had stuff sent from Namibia and South Africa over the years and the cost from Argentina was markedly steeper. Friends have said the same about their "shipping and handling" fees from there.
To add insult to injury, after paying through the nose to ship it, my water buff cape came back from the tannery with major hair slip and unusable. Those are difficult to find and expensive to replace. I have never mounted it and every time I look at the European mount, instead of fond memories, I cringe. For my part, I would not ever consider a return to Argentina. Offhand, I can't think of anything that they will export, that you can't hunt someplace else.
Sorry for the negativity, but that was my experience. Your results may vary. But, if you go, I would suggest you clear any concerns with your outfitter beforehand. And maybe use a hunting consultant. You may need all the help you can get later. International hunting is an adventure in its own right. Argentina may be just your kind.
I have seen some other reports on exporting the native species being a problem. I will check into that further with the outfitter.