okay, here is a response that is not just based on personal experience about sick gloves:
First off, yes, the Burton AK top of the line is nice. Definitely consider it. Other considerations are: Hestra gloves. They are an old glove company that makes REALLY nice stuff. I was lucky to snag a pair last season for cheap ($50. hey, they cost $110 new). They are really well made and super warm. The ultimate mountain glove by Marmot, whoever suggested that, is also a nice choice. Lastly, as someone said, if you don't care about style too much, I had some down mittens which were amazing. I would highly recommend them.
I have the same circulation problem, and here is a HUGE tip that my doctor helped me with and changed my hand warmth: how warm your hands are is contingent on how warm your arms stay. Wear underarmour type gear or other stuff that keeps your arms warm.
I dream of winter.