If you do your staining in a conventional way, it think it's near impossible to make a good line. Most stains are designed to penetrate, so no matter how well you have things taped off the stain will leach under it. IIRC there was someone on the forum who was able to make a good line but I don't remember how they did it. The binding should help make the line however, unless it has some cracks. If you have the binding well taped the stain should not go under the fine-line tape on the binding. You might try a small section by the heel to check first...
That crowning file should work well. I have the three sided version from them which I have been pretty happy with.
FWIW You may not want to leave the masking tape on the guitar too long. I try not to leave regular masking tape on wood or paint. It's generally OK for short periods, but the adhesive is stronger than blue or green painter's tape and can pull paint off, or even veneer off, if you are not careful. Also the adhesive can leave a residue, particularly if your climate is hot, humid or you leave it on for too long. I actually don't like to leave any sort of tape on for very long... Here's the way I did my last one. I had already painted the top and was doing the sides at this stage.
You can't see it in the pic, but the binding has blue 1/4" (6mm) fine line vinyl tap on the binding. I found a to-scale PDF of an ES 335 body which a printed, cut out and used as a cover. The blue painter's tape is stuck mostly to the vinyl fine line tape and the paper. I tried to have as little as possible of the tape stuck to the paint. Even then I only left the tape in place for a few days. Long enough for the paint on the sides to dry, but not long enough for it to cure.