How to make ⌘⌫ delete a line of text in Messages?
You can change the shortcut for "Close Conversation" to something else, that should avoid the conflict. To do this, open Keyboard Preferences, and then go to the "Keyboard Shortcuts" tab. Click Application Shortcuts, then the + button to add a new one. You should get a popup like this one (I'm still on Lion, but I don't believe they changed much):


Change the application to Messages, enter the proper menu title (if it uses an ellipsis, you may have to enter that exact character — not just three periods — by hitting optionshift;), then enter in a shortcut you're unlikely to use.

It's also possible to disable a keyboard shortcut from the command line, rather than just setting it to some obscure command. However I haven't tested this on Mountain Lion or Messages app, so no guarantees.

If you're comfortable with the command line, the proper command would likely be defaults write com.apple.Messages NSUserKeyEquivalents -dict-add "Close Conversation…" nil. However I don't have access to Mountain Lion, so the com.apple.Messages part is just a guess. You may want to test first by trying defaults read com.apple.Messages and see if it pops up with an error. It should spit out a long list of plist-formatted preferences, if it doesn't the app identifier (com.apple.Messages) is probably wrong, so you'll need to do some digging to find out what it is.

Again let me stress that I haven't tested this second option on Mountain Lion or Messages at all, it's just based on how things work in previous versions of OS X.