Personal blog of Dorji Wangchuk alias Kuliśeśvara (Germany). It is for pure speculations and reflections.
I wonder. It does seem to be uncommon, not much result from a TBRC search (a lot of 'false positive' matches). Was thinking that that kha could in every instance have a sense of something 'on the surface' or 'superficial.' Generally brgyud is transmission of deep and life-changing precepts, so the addition of the kha would emphasize that just the opposite is intended, a transmission of stuff that doesn't go deeply into anything at all, just floats there on the surface without disrupting the usual sangsaric flow. I'm not sure my idea is correct, but it does seem to work well to translate 'superficial transmission' in all of your examples. And if that's so maybe there is something to my just-given suggestion, superficial as it may seem. Here's to business as usual, although I hope things will not go back to how they were.
Dear Dan, thanks a lot for your comments and suggestions. So you are thinking of kha in the sense of “surface“ or “superficial” or “superficially.” I am not sure if this would work. But at any rate, keep safe and well. D.