Since I am building modular layouts, the idea of the lights spanning multiple modules didn't really work when I had to take the modules apart, so I needed to make the frames themselves hold the LED strips.
That meant that the wiring to power these lights also needed to be more modular, so I installed these blocks at each border and just fed small jumpers across. The wiring for the LED strip was routed through the interior space of the aluminum frame members (not easy to do, but does give a nice clean presentation).
To power all of these light strips, I bought this dedicated power supply. It gets quite hot, and the 120-volt connectors are in the open, so you have to account for that in your installation, but it works great.
As I continued to work on my layout, I noticed things were getting darker and darker. At first I blamed the LEDs, then perhaps my eyes. One day it dawned on me that the bright colors of the bare wood of the framework of the modules had slowly been replaced with dark green ground cover and black ballast. My conclusion was that the light was being absorbed by the dark colors of the layout. So, I built several more light frames. I had thought about that possibility, so the power supply shown above was rated at handling the maximum number of frames I thought I might built, plus some extra headroom.
The diagram below shows a side profile/cross-section of my overall layout. The brown part represents the cabinets upon which the layout is placed. The green part is the layout (the modules). The blue parts make up the overhead lighting system, the topic of this page. The dimensions are in inches. The horizontal frame piece that is marked as 54" actually wound up being 55-1/4" due to the section where the LED strip can be cut. That piece, measured from its top, sits down 10" from the top of the vertical member. The angled support brace is 33" long. As designed, the framework for the lighting just fits under the 8-foot ceiling of the room. I made it stick out over the front of the layout somewhat (by ~7 inches), so that it could light up the front edge of the layout, as well as the drawers in the cabinets below the layout. These lights are also used as the general lighting of the entire room. The ceiling fan with built-in light is not used in this room, but I didn't feel like taking it down (and having to put it back up again in the future). I did wind up removing its bulb and lamp shade, because they got in the way.