I applied a new prefix to denote which ones would be moved, and which ones would remain.
After all of this, I expected to be able to remove the thread prefix as a mass action, but this does not seem possible.
The suggestion is to be able to remove thread prefixes from the found threads. I could do this using Inline Moderation, but it feels as though the option was left-out from the actions page (it was available in the search page).
Another reason to support this is, to my knowledge, the Inline Moderation tools are not designed to support changes to large numbers of threads. The "Batch..." tools are.