Firstly, there's no reason for you to lose confidence in LED lighting technology or fixtures, especially based on that other thread. Because of the varied opinions, and depth of knowledge, issues get torn apart "7 ways till Sunday" (is that still a phrase anyone uses? ) I use LED recessed lights with great success. To really help with your light concerns, a couple more sizes and dimensions will help. Clarify that the above measurements are height from counter to ceiling, then what really matters is the size and layout of the counter space being lit. A floor plan would be best that shows the counters, wall cabs and any other obstacles. There's nothing wrong with using LED instruments for your lighting needs.

Only you can tell how far apart to space them, because each light is different. I assume they are individual pucks. They throw a cone of light, but how wide that is at whatever distance they are from the surface is something only you can determine with experimentation.

Personally, I prefer strips rather than pucks (I have both). Pucks make little pools of light on the countertop with fairly well-defined edges. The strips work much better for task lighting (and the shadows are softer).