I don't want to go too far out on this limb, but I think it is safe to say that "that said" is dead. As far as cliches go, it is not that old, but it is a dog that's had its day. Why?

In general practice, most speakers throw it into a rambling statement like a kind of bomb.  Think of an account manager speaking about a course of action, only to pause, add "that said," and then abruptly change directions.  For example, "We will be focusing all our effort on selling our widgets to a tightly defined niche of people in Atlanta with deep pockets and no nearby providers; THAT SAID, it would be interesting to see how we play in Cleveland."  Notice that everyone within earshot who still has a job will register blank concern--their eyebrows will rise to compress their foreheads into furrows of inverted "Vs" while the speaker blunders on, unaware of the bomb. Those who have lost interest in the extremely unsatisfying game of following crumpled logic will recognize this as the blather of a person who never considers the listeners or even the subject, which changes like colors along the side of a dead, but iridescent rainbow trout in the hands of a curious child. While the (fading) iridescence is interesting, the brain behind it is, well, dead.  Just like the message.