@Dag-nabit: I sharpened my PXL using a DMT DiaFold Coarse/Fine by freehand and the pictures you have shown seems to prove that my sharpening style leads to a V-edge.
I was thinking of getting a S1 or A1 but held back due to my lack of flat stones (diamond or waterstone).
Does anyone of you think that a DMT Diafold with freehand might work on these convex-ground knives?
I'm a fan of convex sharpening, but I honestly believe that the best way to sharpen is whatever system gives the desired results for each individual.
If you are getting satisfactory results with the DMT Diafold on your other blades, I see no reason why it wouldn't give you the same results on a Fallkniven, or other convex blade.
I have no hands on with the DMT Diafold, but two things to remember:
1. Fallkniven's own site recommends freehand sharpening with a diamond/ceramic stone or rod system.
2: When freehand sharpening it is impossible to hold an exact angle every pass, so you inadvertently create somewhat of a convex edge anyway.
So the short answer is yes, I think it would work just fine on an A1 or S1 if it is working well for you already.
I will put in a bit of a plug for convex sharpening. Sandpaper is cheap. It costs very little to pick up a sampling of grits from about 220 through to 1200 (even going just to 600 will give good results). then use a mousepad, or lay a piece on a leather strop, and give convex sharpening a try. I found it very easy to learn, and even if it doesn't pan out, it hasn't cost a bunch to try it.
Kevin