Now, as I think about it, "tate" seams just means "shield" in japanese
It's hard to find any evidenve of it's existence indeed. Look at this:
http://cis.k.hosei.ac.jp/~F-rep/Haniwa_EGUK2002.pdf
I'm not convinced about katana - it's described as "one and half handed" (like broad sword) and IMO it was mostly used with both hands. Look at today's martial arts like kendo - main arm moves the sword and the hand of the secondary drives it.
One handed use don't let for finese technique (with such heavy weapon) and have sense only with second blade for parrying (and then there is no need for shield).