When you get older your students get older too and you can learn from them!
Yesterday on tachi kumiuchi seminar at the Bujinkan France in Vincennes I learnt two things. One of my old students followed a few seminars to become a blacksmith.
I was teaching the particular way of waving the blade horizontally and was telling the students that the point of pivot is done around the first third of the blade. He told us that the sôri (curve) of the blade is not the same in a tachi and on a katana. The katana is balanced more or less at the middle of the blade but the tachi is often balanced at a point closer to the tsuba. The apex of the curve being closer to the hands it is logical (ans easier) to turn the blade from this point adding more momentum and speed to the blow. Remember that you do not cut with the blade but only try to get uke‘s balance. Also the burden of the yoroi makes it also easier to move the blade that way.
Rotate your blade on itself and do not pivot from the kissaki (tip of the blade). A tachi is not a katana therefore your movements have to be different.
Also, you can find the same blade displayed with the katana mouting and the tachi mounting which confirms what I was writing in a previous post.