Thanks for the quick reply, windguy!
I just measured the tracks, and the extruded aluminum portion is 80" long, and 1-15/16" wide. Looking at them in person, you are right that they are simply too wide to fit flatly in the channels. The seller said something about this being one of the first batch of imported transit connects in this newer body style, but I don't know much more than that, yet. I just took delivery on this Wagon a couple days ago. You are correct that the headliner blocks access underneath.
If not Yakima tracks, I wonder what they are? The previous owner mentioned something about Yakima had been one of the sponsors this car's customization, and I can add that this car came with loads of Yakima hardware and equipment (skybox, bicycle carriers, fairing, round cross-bars) mounted above these tracks.
The tracks appear to be screwed down by a fairly large number of rather common looking, e.g., electro-plated silver Phillips head screws. I could see at least a spot or two on each track where a hole was present all the way through the sheetmetal, but screws were missing! Seems like an obvious pathway for water to be running in, so at least addressing those open holes will be a no-brainer.
It was hard for me to tell if these holes were simply drilled, or threaded. As lighting was poor, I was looking through the (installed) rails, and it was dark outside, I couldn't get a very good look at these holes in the sheetmetal. I'm pretty sure I didn't see any raised lip above the sheetmetal around the hole, like I'd expect if there were nutserts installed.
Maybe there were originally screws presents in these open holes, and they stripped? Sure looks like a screw used to be there.