Yes, you can solder the feeder wires to the sides of the rails. (The
outside sides, obviously.)

In fact, that seems to be the preferred method for some modelers, and as you point out it's about the only way to do it once the track is laid.
And while you're soldering the feeder wires, you might as well solder the rail joiners as well--then you'll only need the one set of feeders.
(I'm a disaster waiting to happen with a soldering iron. So if I can do it, just about anyone can...)