Yeah, the HD 'Economy' stone is pretty aggressive; both sides are pretty coarse (one is coarser), and the silicon carbide abrasive will eat simpler steels up in that larger grit size. Combine that with the softish steel in the SAK, and it'll be hard to fine-tune the edge to a degree you'd likely want. Using a finer grit should make the difference. A 'medium' ceramic, such as Spyderco's brown/grey, would work as a follow-up step. A Fine/EF diamond hone also works very well in it's own right, beginning to end. I've found a DMT 'credit card' hone in Fine/EF to be a good match for my Victorinox SAK blades. Even at these very fine grits, the diamond can set a bevel very, very quickly on the SAK's thin blade. Some stropping with green compound on thin/firm substrate like thin leather, paper or wood will clean up the burrs very quickly. Don't over-strop these blades, as it's very easy to take the 'bite' out of the edge by doing so. All of this boils down to the fact that it's very easy to abrade the softish and low-wear steel in these knives, so a finer grit will go about it more gently. That'll give you some leeway to fine-tune the finished edge, and you still won't be penalized too much in the time spent doing it.
David