Just to throw this into the mix as really it's my main personal question or maybe not even a question really but view. Why the sword?
Using tsuki as your example I equate that more with the spear.(Thrusts)
Tegatana 'cuts' with the sword. Circular with the jo.
Yes, I agree agree completely with that Graham. The Jo Choku Tsuki is a much better example for a parallel with a hand tsuki(punch). We actually learn how to do te gatana shomen by applying the sword principles to empty hand and we learn how to do a correct empty hand tsuki by applying the Jo principles (and as you very correctly said the circular movement that it incorporates).