Made 4 character transfers on classic era.
Two of them completed in about 30 min.
Two of them are now at over 30 hours and it still says estimated time is 35 minutes.
I admittedly didn’t check my mail on these characters as I haven’t played them in months.
File a ticket for “Problem with purchase” and check the mail first next time.
Yeah, I figure I have some gold-seller spam mail or something. But why would that ever be a problem? 
You can submit your ticket here: https://us.battle.net/support/en/help/contact/1995/ticket
It just borks it out. There is a checklist of things to check before initiating a transfer and no mail is a big one. But submit your ticket there and they’ll help get it figured out for you.
Best of luck!
There seem to be some issues with Free Character Transfers that have started in the last day or so. The dev team is looking into it. It looks like that may be the root cause here, not character mail this time.
Please leave your ticket open!
The Free Character Transfers that were lagging behind should be catching up now. Sorry for the trouble folks!