drop a few missiles or shells from a ship on the fuel dump at Ascension,and the threat of reinforcement becomes negligible. Add a prolonged period of winter gales or fog and the reinforcing aircraft would have to divert to Argentina
I'm quite sure that the US Goverment would galdy loan us a couple of CVN Battle groups after said attack on a US owned facility. That's the carrier shortage dealt with. As for the divert there are a few Airfields in Chile that can handle Typhoons and tankers. Read
this.