Aeroparque & LAN
Are you in Bs.As.? Might be worth calling LAN's office. I've never had any luck getting seats ahead of time when combining AA and LAN, but your case is different.
I'd leave plenty of time at Aeroparque. When I was there in November, it was a madhouse. Check-in lines of 60-70 people. They've done some construction since then, so things might be better, but I wouldn't risk it.