I don't know of anything that can speed the process up

apart from chewing on different teething aids, whaich you say bubs doesn't like.
Maybe you could try to make the teething toys more appealing by dipping them in a very watered down glucose & water, the nurses in ER used it when our little one went in and she just stopped crying instantly and just wanted more, and that was whilst they were trying to get a canular into her little arm.
Magic stuff!
Cheers and good luck
Josh