Echofon for Mac →
Echofon for Mac is a Twitter client that, as far as I can tell from my brief 10 minute use of it, honours what I asked for in Unread Badge: I can turn off automatic syncing, and I can control what I want notifications of (ie. I want notifications of mentions and direct messages, not the general timeline).
This might very well be the Twitter client I can settle for.
(Via Leo Laporte on MacBreak Weekly.)