As a note to myself and any other DDWRT-wielding Namecheap subscribers, the correct format for the dynamic DNS setup page is this:

• DDNS Service: Custom
• DDNS Server: dynamicdns.park-your-domain.com
• Username: makesomethingup
• Password: [your really long Namecheap DDNS password (click the Dynamic DNS button on the left side of the Namecheap management page to grab it) - this isn't your Namecheap account password!]
• Hostname: mythirdleveldomain -a my2ndthirdleveldomain -a my3rdthirdleveldomain
• Url: /update?domain=mydomain.net&password=lotsofnumbers&host=

Keep the url blank after host! You can also set the update interval to 1 (updates everyday). Click Apply Settings and watch it go!

Edit: I recently found that the -a parameter in the hostname field allows multiple host updates.