(even though it is a bit after the facts as you just returned...)
We also used Quark, as a means of transport to get to Peter I, on our first expedition, on the Kapitan Khlebnikov. They were very professional to deal with, even though our demands were complicated (we had 12 tons of cargo to be offloaded on a remote island, etc...) Highly recommended (Quark that is, not the 12 tons of cargo).
We returned on the Akademik Fedorov, from AARI... They also take paying passengers, but their schedule (as probably many ships in the Antarctic) has a lot of variations...
The second expedition, leaving from Reunion, we used the Marion Dufresne from IFRTP (the french antarctic research vessel). There our demands were even more complicated (our destination, Howland island) was WAY out of their route, and that time, we had 20 people and 30 tons of cargo. They were also very professional..
Some stories of those trips, I posted on
http://theroadtothehorizon.blogspot.com... The full story of the Peter I trip (even though in Dutch, but with loads of pictures), is on
http://verslaafdaandehorizon.blogspot.com with links to my flickr picture library..
Overall, both trips were adventures of a lifetime, and even though both expeditions cost me an arm and a leg, I would not hesitate for a second to do them again.
Peter