In a situation like yours, there's a few things I'd do. First, I'd make a square feather strip, by square, I mean the front and back side of the feather strip are equal to each other, no bevel! Then, I'd make it about 1/2" above the height of the rail, and make it fit the rail snug. Then I'd wrap the feather strip in magic tape, you know, clear scotch tape. Then, I'd tap the feather strip into the feather strip dado, sinking it to the bottom of the dado. With this feather strip in place, fill in the missing wood from the rail with bondo, flush it to the flat edge of the rail, and up to the feather strip. Don't use to much hardner, it'll dry to fast, and be to hard to work with. You're going to have to fill it in at least a couple of times. Once the bondo drys, then remove the feather strip, the bondo won't stick to it because of the plastic scotch tape, then make new feather strips that actually fit the dado.
Glen
PS. Bondo works better for repairs like this, than wood putty does. Wood putty drys on top to the touch, but takes for ever to dry deep down.