You can use 'Messages Customiser' to hide the settings (along with the search), as well as other visual theming and tweaks. It works with both iMessage and biteSMS.
You unfortunately wont have access to settings easily anywhere else, it will need to be unhidden again. But it doesn't need a respring or even to close the app, just go into a conversation and back out again to refresh.
The particular setting you're looking for is in Settings/Messagaes Customiser/Convo List Settings/Hide Search Bar.
Incidentally 'Unread' (a manual unread indicator) works with biteSMS along with iMessage and I'm sure other tweaks will too.
I know that doesn't help with the original problem. I'd quite like to know the answer too.
As a workaround would it suit you to hide all app labels. Overkill maybe but it would solve that problem at least.
Maybe something editing a .plist iFile/SSH would do the trick, though I don't know if that could cause problems. Doing it through Winterboard could be better assuming biteSMS haven't blocked that also.