Update:
As noted, I received my replacement product last Saturday. The new watch is still working without any issues. I swear it runs faster than my original device, but that's probably a placebo effect (No, they didn't replace it with a Series 2, for anyone wondering).
Today I was finally able to connect with my Executive Relations contact after some phone tag this week. I noticed AppleCare+ didn't seem to properly transfer to my new device (or seemed like it was still a work in progress online), so he is looking into this item for me - I'm sure it will be resolved without issue. What really blew me away, is that I am now being awarded a ~$200 "good faith" gift on the Apple Retail Store for being a customer. Really glad this is offered in lieu of my wasted time on this issue, and unnecessary time without my product.
In the end, really thrilled with how Apple handled the situation.