So that's argument in favor of the "slow transition" premise?
No. "Slow transition" is just hand-waving to avoid the issue.
Imagine that you and I have identical buckets. Imagine that your bucket is full of water, but mine is empty. Imagine that you pour the water from your bucket onto hot coals and it becomes steam. Imagine that I fill my bucket with water from the sink. Is it fair to say that the water from your bucket teleported into my bucket? No, of course not.
Now, imagine that we have the exact same setup, but rather than
pouring your bucket of water onto hot coals, instead you scoop it out one handful at a time and pour only a handful onto the coals. And every time you do, I fill one handful of water from the sink and put it into my bucket. One handful at a time, until your bucket is empty and mine is full.
Does doing it this way cause the water to teleport? Of course not.
So why would slow transition result in your consciousness being uploaded?
The whole "copy your brain to transfer consciousness" idea is predicated on the completely arbitrary assumption that consciousness is an emergent property of a configuration. Not "of" anything, just "a configuration."
For example, think of a book. How about, the Velveteen Rabbit. That's "a book." But when we say that the Velveteen Rabbit is "a book" we don't actually mean that it's a physical bunch of paper. Really, it's "a story." For example, if you have a copy of the Velveteen Rabbit on your nightstand and I have a copy of the Velveteen Rabbit on my nightstand, we'd both probably agree that both your copy and my copy were "the" velveteen Rabbit. And, if you burned your copy and downloaded it to an electronic tablet, we'd both still agree that the electronic copy on your tablet is still "the" Velveteen Rabbit.
"The Velveteen Rabbit" is a
configuration. It doesn't really matter if that configuration manifests as ink on paper or electrons on a screen or words being spoken by a storyteller talking over a campfire or table entries in a database, or whatever. It's still "the" Velveteen Rabbit. Even if you translated the words into Chinese and encoded paragraph and page breaks with HTML and stuck in on a web page, resulting in all the individual characters and words being completely different, it would still be "the Velveteen Rabbit." Right?
The "copy the brain to upload" crowd apparently believes that consciousness works the same way. For some reason.
I see no reason to believe that.