I wasn’t aware that character transfers for Classic were already introduced. Beyond the free ones they have offered from high pop to low pop-- those are predetermined by Blizzard. They typically always stick to servers of the same type in these situation.
If you’re on a high Pop Pvp-- They will pick out a low pop Pvp server.
But I certainly would check with Customer Service Forums. GD can’t help you with this.
Edit:
Pretty much states they only opened free transfers from PvP to a new PvP. You’ll have to re-roll.