Hi. I once wrote some instructions on how I do binding, with emphasis on prepping the channels. Channel prep is everything when it comes to installing the bindings and purflings, and making it look professional.
I have tools you probably don't have, so I'll tell you what I use, then give you a great alternative.
First and foremost, you need to use shellac on your channels. Really saturate them. It's easy to miss a small spot. I put 2-3 coats of shellac in them. Don't worry if the shellac gets on your sides/back/top. You should put shellac around your top anyway, because it'll protect it from dark sanding dust. Shellac also imparts beautiful 3D appearance to side and back wood, unlike other finishes. It works well under all finishes, water or oil based. Zinser from lowes or home depot works fine. You can buy flakes and make your own. It doesn't matter.
After the shellac has dried, let it go overnight, Prep your channels. I use an Iwasaki Razor file. There are several shapes. The one I use the most is the 150mm straight file. It's like a fine rasp, but leaves a finish like sanding. Both edges are safe and Both sides cut.
Prep one channel at a time. You need to prep BOTH surfaces. Keep whatever you use straight to the wood. Go gently and take your time. Let the tool do the work. Good prep can take quite a while.
Since this is a straight file, you'll find it doesn't do the waist channels. There is a curved file as well. But, I've found that the very end of the straight file works Iike a scraper.
As I said, there is an alternative to this tool. You can use a scraper (the rectangular one) or razor blade. The end and corner of a square ended 6" ruler works great. You'll find that the shellac allows for easy removal of those fuzzies. It's also preps your surfaces for glue.
So, after scraping or filing both surfaces of your channel, test the fit. Cut a 1/2" piece of your binding, and run it along the channel. Look at the fit. If you find a place that's not deep enough, from either direction, use your file/scraper to widen or deepen it in this area, until your piece fits. Once you see a good fit all the way around, do the same steps to your other binding channel, testing your fit. Then turn your attention to the purfling channels, performing the same steps as you did to the binding channels.
I always go very slightly deeper on the channels than the wood. It's better to sand the wood to the bindings/purfling, than to scrape down binding. You want the bindings to be of even thickness and width all the way around. When you start scraping bindings, some areas can get a little thinner than others, which is noticeable.
This is my file:
https://www.woodcraft.com/products/iwas ... e-fine-cut
