I was just in Ushuaia 10 days ago, and the lowest prices for last minute spaces on Antarctic ships was US$3,300/person. Depending on which agency you book from, you can also have a jacket, boots, etc. thrown in for the $3,300. For single travelers, you'd be paired with one or two other people in your cabin.
Getting to Ushuaia using miles shouldn't be too impossible, as LAN serves USH from both SCL and Buenos Aires (AEP, not EZE). Aerolineas Argentinas and
LADE (the cheapest option) also serve USH from AEP. Flights are about $160 each way from Buenos Aires.
There are various inexpensive hostels in Ushuaia if you're really trying to save money, but book in advance as they fill up fast (even late in the season). I stayed at the new
Hotel Península Antártica for US$116/night.