Sorry to continue asking questions, but I have a few more. I tried sharpening a kitchen knife last night with only slightly better results, and really want to make sure I'm doing this correctly and have reasonable expectations.
First, should I be using multiple near-perpendicular strokes to maximize the blade "slicing" against the stone (similar to what the DMT manual shows), or is it better to make one sweeping movement across the length of the blade?
For the initial grinding of a new bevel, pretty much any stroke will do. At that stage, before the edge is apexed, it's all about grinding off lots of metal. Many like to use a back & forth 'scrubbing' stroke for this (I usually do). Once the new edge is apexed, I'll use edge-leading sweeping strokes (heel to tip), to even out the scratch pattern. Then do the same with the subsequent hones, all the way through the finish.
Second, what would be the best type of knife to learn on? It sounds like the SAK may not be the best bet, but I'm really hesitant to try it out on my Spyderco Native until I'm convinced I'm doing this right.
I think a simple kitchen knife of known decent steel quality is always a good 'practice subject'. If not that, then a mid-line pocket/fixed blade in carbon steel or one of the middle-range stainless steels (420HC, 440A/C, AUS-8, etc.) are also good. Try to find one with a similar blade size/thickness/profile as your SAK's blade, if possible. That'll help get your hands accustomed to the feel of the process, for the blade you want to sharpen.
Also, for practice's sake, use only a fine/ef diamond hone to start. Since you have the DMT EF (green), I'd practice with that one first. The finer grit won't be quite so aggressive, and that'll be a little more forgiving on the steel, while you're still trying to refine your technique. It's too easy to do a lot of damage in trying to 'practice' with a very coarse/aggressive hone. And the finer grit will slow the process a bit, which makes it easier to detect changes in your edge as you go.
Finally, what would be the best litmus test for she sharpness of my kitchen knifes? I didn't get it shaving sharp, but having it that sharp probably wouldn't be appropriate anyway. Should I try the blade against my fingernail?
My favorite test for any blade I sharpen, is to slice phonebook pages. The paper is thin, and folds/catches very easily on burrs/wires on the edge. This is a great way to look for these imperfections on an edge. When I cut the paper, I'm looking to slice cleanly and repeatedly through the paper, from heel to tip, without snagging in, or slipping off of the paper (slipping indicates the edge is blunt or otherwise not completely apexed). If the blade catches and folds the paper, look very closely to see where this happens on the edge. Slice very slowly, so you can more easily see where it catches. That's the place to look for a burr on the edge.
The 'fingernail test' is handy for looking for wire edges that are folded or leaning to one side or the other. I gently angle the blade to one side, and then the other, while gently touching it against the broad portion of my thumbnail. If the edge catches when leaning one way, but slips when angled the other way, that's a good indicator that a wire edge is present, and angled in the direction that the blade is slipping. If it slips in both directions, that usually indicates the edge isn't apexed (it's round/blunt). Conversely, if the blade catches in both directions, and all along the full length of the edge, that's a pretty good indicator the edge is in good shape.