0.6 mm isn't exactly thin behind the edge, and this might even be part of the problem.
If you're not overly attached to your knives current appearance you might consider a slightly convex regrind (this can also be done by hand using wet & dry SiC paper on glass), and then use a microbevel for the actual edge at ~30 inclusive/ 15 degrees per side, for instance on Spyderco medium or fine sticks.
Not only will the difference in cutting performance be dramatic, touch-ups will also be very fast & easy.
Most of my kitchen knives & peelers in softer steel are done this way, and the ones who still have a standard edge are ~0.2 mm behind the edge.