To address your worry about the strength of the bottom, you could add another false bottom inside the cabinet. This would also give you a place to run wiring discretely. See this article which explains what I'm talking about...

Retrofit Undercabinet Lights in Frameless Cabinets

How modern or traditional is your kitchen? In our modern kitchen, we also had no light rail, and installed LED tape by inspired led dot com. When we decided to cover it because you could see it when sitting on the sofa in the adjacent living room, we used brushed aluminum Shluter (the stuff that's normally used to trim tile). I'm on a plane now and don't have a picture handy, but if you're interested I can post one later.

DIY2 - that's a great article! What it describes is similar to what I was thinking - using IKEA so I thought we would use an end panel to create a 1/2" height rail - but your article suggests using a full panel (laid flat) and cutting into it for the lights - that's probably a better option!

hockeyfan - The kitchen will be traditional/farmhouse. How do you like the inspired tape product - is it bright enough? I looked at that as well. Your comment about seeing the lights when seated is a valid concern. We will have counter height seating looking directly at the cabinets so that's why I feel like we should add something to make the lights and wire less visible.

I really don't like the IKEA deco trim - it fans out (Bodbyn) and I just know it will get banged up - then there's always the problem with making good miter cuts. And, I want to have as much distance between the counter and cabinets as possible.

The Inspired LED tape lighting is fantastic. Very very good light and great customer service. I know it won't work for you (too modern) but here's a couple of pictures. The light you see is the only light source. The top picture is with the lights off (the light to the left is from the hood).

Looks great hockeyfan! I did send an email with info asking for a design, got a reply letting me know they were working on it and I should hear tomorrow.

I used these LED strips from Environmental Lights. They are basically covered LED strips, in a sturdy lensed housing, and are .4" deep. The product and customer service were both very good. No affiliation, just a customer.

ENVIRONMENTALLIGHTS PREMIUM MODULAR LED UNDER CABINET LIGHTING

I mounted them directly on the bottom of the frameless cabinets, 3" back from the face of the box. I used a 2" x 3/4" trim piece to hide them. We have counter seating and the light source is not visible. A 1/2" piece might work... you'd have to try it.

They also make a "high brightness" version, but these provide more than enough light. They are controlled by an inline touch dimmer.

DIY, thanks! I actually used Environmental lights about 5 years ago when I did my main kitchen and thought they were great! When I checked their site recently I was disappointed to see fewer sizes, especially in the warm white color. Not sure if I was looking at the super bright or no, but I will check again, Your trim piece as a light rail is exactly what I plan do do but I want it as thin as possible - IKEA side panels come in 1/2" thickness so that is what I'm hoping to use. Love your kitchen by the way!

I used Hafele Loox purchased a couple of years ago and the track is actually smaller than 1/2 inch.