Really nice job! You are correct in the hindsight of staining the wood first. Likewise painting the wrap and trim accents first (then touch up after install) makes life a bit easier.
Great job. One warning: I was helping a friend do some renovations, converting a 20' x 20' barn into a dog training studio. We originally installed similar lights. We put them in before the sheetrock was up, tested them and they worked. We disconnected the light part after testing. The electrical boxes were secured to the trusses. We started insulating the ceiling at the far end of the building. Power in the building was on so we could play the radio. Before we finished insulating the ceiling, one of the electrical boxes from those lights started smoking and sizzling. We opened the box and looked to see if we made a bad connection when wiring it. All connections looked good. We removed all the lights and bought metal ceiling boxes and conventional external mount light fixtures. In fairness, we were using 12/2 exterior grade wire, and those boxes that come with the lights are kind of small for wire of that heavy a gauge, but we didn't see any signs of bad connections on our part - we think the smoke came from the tiny transformer in the unit.
so short (width) towards the front on the slats. You'll say it didn't matter because you'll cover it up (of course) BUT . . . . . . Using molding where you don't have to, because your measurements are more precise . . . makes a cleaner look. No?
I love the look of the cedar when it is newly installed. But doesn't it turn gray as it weather/ages? I realize the ceiling of the entry won't see direct sun or rain, but I did see you used it in other places where it would. Are you using a finish that prevents that?