If you are in fact a doppelganger you have no way of knowing and neither does the Anomander who died. And that is why I wouldn't risk teleportation.
Which, conversely, is also why I don't care about teleportation. If I have no idea before and I have no idea after and for all intents and purposes I am still me in the new location ... all the parts that I can engage with, all the parts I care about - they're all coming up fine. I might as well have fallen asleep on a plane, or blacked out after a few too many at the pub. When consciousness returns, I am in a new location.
In that explanation you quoted, I fall firmly into the former camp. I don't think we have special-ness that transcends the meat, but that the consciousness is wholly rooted in it - and so I think that moving the meat from one place to another achieves the result of moving the consciousness from one place to another.
My main difference is that I don't believe a "soul" transported or transplanted - or exists to be lost. The consciousness that is my sense of 'self' is the sum of my meat and my memories, and those are preserved.
Tumblr remains impressively Not Dead given its ownership and finance history.