I have done this and cut hole for a single gang box in cabinet above where you need wire and then cover with a blank plate. Grab wire thru single gang hole and then feed it down to 1/2" hole then cover single gang hole with blank plate.

What also works is chain. Drill the hole in the top plate, the chain will easily hang, and it's pretty each to grab ahold of with a coat hanger. However, I don't think it's code to put a receptacle like this on a backsplash.

You cannot have a receptacle for the UC lights in the backsplash under the cabinets.

They are typically put IN the back of the cabinet, with a hole through the cabinet bottom for the cord.

You can cut a hole through the cabinet back, and then the wall to recess most of the box into the wall.

Thanks for the input - sorry I didn't clarify this at first. These are Philips eW Profile line voltage hardwired lights. The NM cable terminates in a low-profile wiring box mounted to the cabinet bottom, and then uses a UL listed jumper to connect to the first light strip.

I believe this to be code-compliant; you can perhaps argue whether the exposed NM cable on the bottom of the cabinet is allowed. The wiring box can be installed at the back edge of the cabinet to resolve this.

The chain flow on the end of a pull string is a good method; I haven't used that before but I should. Hopefully I can get the hole in the top plate lined up just right; if it weren't for the extra cross piece I could swing it back and forth until it hooks. I was hoping to avoid cutting more holes, but if I had to I would.

A short piece of fine chain works.

You can also just run the fish tape past the location and then form a hook into a section if coat hanger (or even broken off fish tape) and then hook the tape from above and pull it to the hole.

It is not all that hard, it just takes time.

There are often advantages to dropping string with a large nut on the end and then hooking it.

Mason's woven string is cheap enough and strong enough to then pull a fish tape from the bottom out the top to pull a cable down.

As long as the lights are hard wired you are fine.
They still need to be on a different circuit than the counter receptacles.

Use a 15 A circuit with #14.
It is a lot easier to work in confined spaces.

I'm an alarm tech and we run alarm wires in situations like this all the time. We use an aviation bit to drill through the ceiling into the attic space at the spot next to the wall where we want to drop the wire, and caulk it afterwards.

Eliminates guesswork. Drill hole through top of wallplate, use chain as suggested, to drop down to where you are going to fish the wire out. Don't buy the ball-type chain, it's too weak, but something fairly fine (not the crap that's folded sheet metal either, it kinks) and steel, so you can use a magnet to attract it - although a bent coat hanger is usually good for fishing, if you have problems, put a magnet on the coat hanger (assuming it's steel) as a hooking aid.

Your helper in the kitchen hooks and pulls through the chain, attaches the wire (securely, tape may make it more streamlined) then you pull it back up into the attic, and you run it to where you need it to go.