I experimented with 'stick on' pucks from Costco... worth a try, battery operated. But -- not much light.

Here's the problem that I found with LED pucks. All LEDs are very directional, so pucks cast a very defined circle of light. You need to be very careful to keep them close enough that the pools of light overlap, because the cutoff is often fairly sharp. You will have dark areas in corners and possibly along the wall. Pucks are fine for high above the sink; a pair of them provide great light, and because of their height the beams spread out enough.

I have plug-in under-cabinet lights on a motion detector; they turn on when you walk in the kitchen.

I have no idea what you mean by front and back (of what?) and X X X X.

Strip lighting is much more even, but I find the lack of real shadows a bit weird.

Not using LED pucks? Beware of heat on the shelf above them. My halogen pucks could melt stuff on the lower shelf of the cabinet (candy, etc.) right above the puck.

Thank you. You bring up some very useful insights. I believe they are LED. I was going to put them under the cabinets in 2 rows, one row close to the back wall and the other row close to the front of the cabinets. Or stagger them one close to the back wall and one close to the front of the cabinet underside. And I agree with you about keeping them close so that the pools of light overlap. Maybe it will be too complicated. I will give it some thought. You bring up some great points.