For anyone else having this problem, here's how I solved it:
1. Went to ZoneEdit and signed up for free DNS Management for lsugnomes.com.
2. Changed the Nameservers WordPress is using for my domain to the ones provided by ZoneEdit. Wait an hour or so for the change to propagate.
(To make this change, go to the WP Dashboard -> Domains -> Manage Domains -> Nameservers)
3. Add a subdomain to ZoneEdit for http://www.lsugnomes.com, as Blogger won't allow naked domains.
(ZoneEdit's UI is not very intuitive, but there's a field on the left to add a new subdomain. Type "www" there)
4. Edit the CNAME and A entries for www to the ones described by Blogger: http://www.google.com/support/blogger/bin/static.py?page=ts.cs&ts=1233381
(Wait an hour for changes to propagate)
5. Edit publishing settings in Blogger to use my custom domain. If ZoneEdit isn't updated yet, Blogger will let you know.
(Blogger Dashboard -> Settings -> Publishing)
6. Finally, go back to ZoneEdit and set up Unmasked URL Forwarding for lsugnomes.com to http://www.lsugnomes.com.
After my 60 days are up, I'm going to just transfer my domain to godaddy. Even though I've got this all working now, I manage other domains in godaddy and would rather not have to deal with WordPress + ZoneEdit for domain management as well.