Yeah this will happen. Depending on what stain you've used you may be able to very carefully bleach it with a cotton tip. Somebody on here carefully masked and painted the binding ivory before clears and it looked really good. Tedious extra step, but the results will be worth it. Hopefully someone will be along who remembers which build diary that is in.

The inconsistent width is annoying, I had this on a non Pitbull build, but I was doing a solid, so just taped and painted over it. You might be able to carefully tape and paint that sliver black and blend it into your stain. Once the clears go over you'll never see it.