I have one other potentially dumb question regarding strokes. It was my understanding that back and forth strokes were used for quickly establishing a new angle when needed, and that once you get to that point you should switch to the tip to heel/heel to tip to actually "sharpen" the blade. Is that true?
In my experience, whether you use back/forth or tip-to-heel, or circular (as some do), it's pretty much a matter of preference. Ideally, when you have the time and opportunity to do so, experiment with whichever methods you'd like to try. You may find one that you're much more comfortable with, and which produces the results you desire.
I use a Lansky and/or GATCO system. They are guided rod systems like your KME kit. With these systems, I generally use a back/forth stroke for every part of the sharpening process (creating the new bevel, forming the burr, and then finishing & polishing the edge), which tends to produce a scratch pattern similar to that of most factory edges (the scratches, or grooves, tend to run perpedicular to the blade edge). For me, a back/forth stroke allows me to focus precisely on those areas/sections of the edge that still need more refinement. As the edge becomes more fine, you'll tend to notice that some sections of the edge will 'get there' much sooner than other sections. With a constant tip-to-heel stroke (or vice-versa), you may spend a lot of time sharpening sections of the edge that don't necessarily need that much attention.
And, for the very TIP of the blade, I find a back/forth stroke (perpendicular to the edge) to be much safer. In, my experience, a tip-to-heel (or heel-to-tip) stroke increases the danger of either running the stone all the way off the tip (resulting in rounding of the tip) or running the edge/side of the hone directly into the tip (resulting in a bent/knicked tip).
As I stated before, for me it's much more important to focus on using progressively lighter pressure, no matter which type/direction of stroke you use. As the edge becomes thinner and more refined, it's important that you lighten the pressure of the stroke, so you don't end up overpowering & dulling that fine edge.
Edited to add:
Let me add this point. I can see, for folks who use benchstones freehand, a tip-to-heel or heel-to-tip stroke more readily lends itself to a smooth, natural motion for sharpening. I don't knock this method at all. But for a guided rod system, with it's relatively smaller and narrower stones,
and the fact that the rod is attached to the clamp/guide at the upper end, I think this setup more readily lends itself to a back/forth stroke (towards and away from the 'attachment' point on the guide).
