Julian, I don’t know if badgering and pestering are necessarily a good way to approach the issue. Like I said, get permission to keep in touch and then do it. Not in a bad annoying way, but in a way that makes them feel that you are a valuable asset to use if everything goes wrong at the last minute.
Also don’t think of October first as a deadline. You could be hired at any point in the season. Summer is from Oct to Feb, but if someone gets ill in November could you be available for December to Feb or even on into the winter?
Another thought on the matter. You might as well give Scott Base a try as well.
The NZ antarctic programme is also located at the International Antarctic Center in Christchurch. There has been at least one American that I know of that went to Scott Base. Also try to get on with one of the science groups as a helper or computer support. Who knows what will drop in your lap.