A type of flooring that would help with both durability and warmth?

Your not going to like my answer, but your best bet is crawling into the crawl space and insulating the floor from from there. It's a dirty job, so you may want to find someone else to do it. Preferably some teenager who needs to be taught why he/she needs a college education :-)

You could use bamboo, cork, or engineered hardwood in this space. Your are right about these flooring options keeping some of the cold out. Any one of these flooring materials can be laid on top of a layer of a sound deadening underlayment. This will act as an insulator. Also, all 3 materials mentioned are also pretty diy friendly. You can even lay any of these over a heated underlayment. This stuff comes in rolls and really isn't all that hard to put it. You basically just roll it out.

The first thing I would do before I decided on the floor in the conditioned space is insulate in the un-conditioned space. This insulation will be what keeps the floor warm in the winter. If I did this, I would probably use cork.

polar bear fur