This is a tough ask - and I don't think that all your criteria can be met!
Jan / Feb is a good time of year to go, but to depart from NZ to the Antarctic continent is a 5-6 day sail in each direction, so if your 2 week max trip length can't be extended then I would suggest a cruise to the Peninsula from Ushuaia rather than NZ, which is only 2-3 day's sail across the (often rough) Drake Passage.
Camping on the continent isn't offered by any cruise companies that I know of, and may well only be possible on a private charter (yachting?) expedition. [If you are seriously contemplating this, then proper survival equipment etc would be required - and please take care to ensure that no adverse environmental impact on wildlife etc is caused...]
Visits to science stations certainly can be undertaken, but only by advance permit / negotiation, and most of the larger Antarctic cruise specialists are able to make the necessary arrangements.
Your wish for helo flights does narrow down your cruise options considerably, as only a very few ships carry them. These are generally the ice-breakers (rather than just ice-strengthened vessels) operated by companies such as Quark Expeditions, and tend to be used on longer (eg 4 week) trips - which of course take you some way over your $10k budget.
But don't let any of this put you off - Antarctica is well worth the effort (and cost) to get there, and even a voyage just to see the scenery and wildlife of the sub-antarctic islands such as Macquarie would still be a fantastic experience! :grin:
Hope this helps...