Unless I'm some sort of exceptional case (which I might be), I would say that there are still bugs in the system besides that 12 toons bug. I'll use my own experience as an example.
I transferred 2/3 characters successfully from Dalborra to Shadowlands on the day transfers opened up to a server where I'd exceeded 12 chars. The third character, my sith warrior has been stuck 'transferring' (according to the website at least) for almost the past two days now. What's weird is his achievements and legacy unlocks carried over, but the character itself is still stuck on Dalborra and I'm able to play him as normal. The website however continues to believe that the character is in the queue to be transferred for some reason so I can't reset the transfer or try again or whatever.
Sending a ticket basically ended up with generic response from customer service explaining how the transfer process works and didn't answer my question at all so I guess I'm stuck waiting until the issue is fixed or until paid transfers open up.
I have made pretty similar experiance. My marauder is still stuck on Dalborra. Already made two ticket and got only less then helpfull Responses. I hope BW cleans up the Transfer process bevore it gets a paid Service. I can only imagine how mad People will get when they pay LOTS of CC for this and then it takes several days until the mess is cleared up.