With that are you drawing the knife across the stone lengthwise? I have always moved the knife along the stone perpendicular to the cutting surface.
Most knives's cutting edges have a slightly rounded shape like the bottom of a boat. I don't know the common term for it, I call it "rocker". Pulling lengthwise you'd have to subtly change the angle as you pull to keep that consistently on the middle of the stone. Going sideways you can feel that the knife is centered.
It seems like the block idea could be useful for sharpening across the stone. Maybe just put it at one end and use it to set the angle when you start.
I am drawing the knife across the stone, exactly perpendicular to the stone, and following the curve of the blade as I go. On a really long blade, I will break it into sections, as I get better results than drawing a long, curved blade in one stroke.
I used to work (for 25 years) in a custom millwork shop, and this action is very similar to working radius pieces on a shaper, face of the piece against the cutters, where you have to keep the part of the workpiece that is in contact with the cutters exactly where the spindle is as you "roll" the workpiece around. I did that type of work freehand, with only springs to hold the work lightly against the fence.
I am still experimenting and hope to move towards not using the blocks. Yesterday I tried using slipstones (about 4" long), freehand along the blade edge, with the blade resting on a clamped down piece of 2x material. That worked surprisingly well. Having done my own pocket knives, my wife is throwing all her kitchen knives and scissors at me now, so I have a good supply to learn on.
Sharpening Supplies is a good resource for all types of stones and sharpening equipment, including all of the brands of sharpeners mentioned in this thread. I don't know if they are the cheapest, but they are a responsive small business and a pleasure to work with.