Im not an expert in sharpening but i think i can help you:
Grippys iirc use a 15º+15º angle (in the sharpmaker you should use the 30º slots like it recommends)
if you use the 40º slots you will be REPROFILING the blade, but with the stones the std sharpmaker provides it will take you a couple hundred thousand strokes.
the sharpmaker is very good for blades that need a little maintenance, but not if you are going to change the angle of your edge, if you want to confirm, paint the edge (just the edge, not the entire blade) with a permanent marker and then sharpen.
what you mention about using both angles is a microbevel, and its advantage is only that its easier to maintain (next time you sharpen should take you a little less time), but that will take an extremely long to make with the sharpmaker.
However, i have a Benchmade Rant that is supposed to come at 30º inclusive, but the blade suited the 40º slots in the sharpmaker better...
my advice: use permanent marker method and see if you are only removing the shoulders or if you are sharpening the whole edge, according to that take the angle that sharpens the whole edge, and then sharpen the recommended way, dont put much force, just use the weight of the knife; but the most important part: be consistent on the angle, try to keep the knife steady and dont roll the tip.
hope this helps.
* the difference in a 30º angle and a 40º one is the strenght of the edge, a 40º inclusive edge will be stronger but a 30º inclusive one will slice better, if you have been using a 30º all this time and the knife has held up great then there is no need to change that, in fact if you change to a more obtuse angle and will use more force to slice, you will have less edge retention and will need to sharpen more often.
**edit: added info on how the blades sometimes come out the factory with a different edge angle.