How can I completely reset iMessage in Yosemite?
I posted on the Apple Support Communities board for help. From the response I learned that removing ~/Library/Preferences/com.apple.imagent.plist clears some Messages app state. When re-launching it, I'm presented with a fresh sign in flow.

In my case, the root issue still wasn't resolved.

In Console.app I found log messages like the following:

2/16/15 3:23:18.011 PM identityservicesd[4905]:
  [Warning] SQLITE_CORRUPT encountered error 11 while accessing
  /Users/mike/Library/IdentityServices/ids.db, exiting!


Searching for that turned up another post on Apple's Support Communities board which suggested removing ~/Library/IdentityServices. This solved the issue I was having, and I haven't yet noticed any unwanted side effects.