@Gargron One important detail that I discovered: Step 2 needs to be performed on BOTH servers. Each server needs have an alias pointing to the other one for the functionality to work.
This is poorly described in the UI.

Then you need to wait an unspecified amount of time (I needed to way a full day) for the two servers to synchronize your profile data and be aware of each other.

THEN you can do the "Move to another account" step.