To measure inductance you need an LC meter, such as this
Digital LC Meter 390-570. A few years ago, I found a less expensive one on Amazon. Poke around to see what you can find now.
All I do is unwind the coiled wire until the meter (attach the leads to both ends of the wire) reads the desired inductance value. As wire is unwound from the spool, it no longer acts as an inductor, so you don't have to cut wire until you have the value you want. After making the cut, I use sand paper to scrape away the lacquer coating from about ½" of the end of the wire so I can solder later.
About the burn marks where you cut the recess for the drivers. I usually use a black marker, like a Sharpie pen, to blacken any visible part of the recess cut. Maybe that will cover the burn marks without sanding.