I live in Utah, but unfortunately there's no way I can take any more dogs.

Here's some places to try though

http://www.utahpets.org They have lists of many rescue groups in the state that may be able to help. http://www.petfinder.com You can put an advertisement for free (not the adoption listings, just a brief message, no pics)
http://www.utahdogs.com It's all about dogs in Utah, they have a rescue section and may be able to help.
http://www.bestfriends.org Best Friends Animal Sanctuary is the largest no-kill rescue in the nation. It's located in Kanab, UT (about 6 hours from SLC) You may try contacting them.

Best of luck to you! Oh, and those websites were just off the top of my head, if any of the links don't work let me know.