Copy the transfer deny link they sent you but delete everything after YOURDOMAIN.COM (&action=...) in the link and then visit it.
Copy the trigger code from the last part of the link you deleted and paste it where appropriate on the page you see. Select action "request" and click on the "continue..." button. This will expedite the transfer.
Every time I transfer out of Moniker.Sounds risky.
Have you done this successfully?