Jake,
Yes, I think you're doing a good job of expressing yourself.
With shorter cuts, use of the lever of the grip of the sword becomes more emphasized, as the goal of any cut with a proper sword is to get the sword to naturally and gracefully rotate around its center of balance so that it does the cutting for you.
Does this require "strength"? Of course. You have to be able to handle the tool. Does it require "intent"? Yes. You do intend to cut them don't you?
The trap in these semantics is that by focusing on these two words, keeping a sharp eye out for them, and jumping on anything which doesn't use them in the same way as one indivual might understand them as bogus, you see the practice of others as different, not as similar. On the other side of the coin, when one is taken to task for not having "proper strength and intent" when they know quite well they do, then they can only assume the criticizing party means that they need to have more (excessive) strength and intent. Misunderstandings and acrimony begin, and continue for years, when one tries to define what they are doing by what it is not, rather than what it is.
Everyone I have ever seen do a credible job of teaching uses both strength and intent. Yet with a sharp, well-made sword, if you move your body through the proper path, as described by the master, you don't need more strength than that which is supplied by the motion indicated by the proper motion to sever an arm. You don't need any more intent than your intention to cut them to make a valid cut. I don't have to power it if I have the proper tool and the proper mechanics.
I hope this makes my particular position a little more clear. Semantics are very often the problem, and when you study ancient languages, you may have no clue to the semantics. In the "fence with all your strength/buffalo" issue, what is really meant? Only someone who has a *very* good knowledge of Medieval German can make an educated guess. I can't, and most of us can't. Hence the seeming contradictions and confusions.