It's in! And it's gorgeous! I'm very happy with our new cork floor in the kitchen and, once again, have to give a big shout-out to Paul, who really did most of the hard work. You saw what we did last night (along with lovely Leslie's help!), which constituted a lot of the "hard" work. This morning, we started at 7am and put the underlayment down and then went ahead and got started.
Below is the first course, which was probably the toughest. It was a lot of making sure it went in right and the cuts, particularly around the heater pipes, were correct. Once that was in, it was pretty much smooth sailing. While the directions didn't suggest doing so, we did stagger the seams, which I think makes it look better and is much stronger.
I would definitely recommend this product (HD ordered - $2.99 sq ft) and this project to anyone. While we of course still will have to put the thresholds and baseboards back in as well as a bit of quarter-round here and there, it's pretty much done. Altogether, it took 3 hours to do the prep work, including removing thresholds and cutting out the door casings. And then about 3 and a half hours to do the actual floor (the kitchen is 13x14).
One tip I would have is to definitely buy the little kit you can find at HD for installing engineered floors. It came with a tapping block, the spacers, and a metal pull bar. It was about $20 and wasn't recommended in the directions but it made the whole thing a lot easier, in my opinion. Besides that, it was just a jigsaw and a circular saw to do the rest. Easy-peasey.