I did the exact same thing you're thinking of doing, but the Eternabond had trouble sticking to the irregular surfaces of the inside track, screwheads, etc. The flathead screws, countersunk, do help, but there's still a lot of irregularities there. So I bought some "doublesided" Eternabond tape, ran a strip of that inside the rail over the screwheads, and then lapped the white Eternabond down over double-sided tape down to the bottom lip of the rail. Having that extra thickness made a big difference in how smooth the finished job turned out to be.
Good luck!
Regan