@goosehd I finally worked up the courage to try this, and yes, it totally works with a seam ripper. I also used tweezers to pluck away at the threads and bits. Thanks @Mister_Brue for the tip.
For anyone else trying this, the key is that the label is made of a much more fragile fabric than the stitches or the denim, at least on my IHSH-293-OD. Just have to slowly and carefully fray the label and it will gradually break away as you use the seam ripper to break up the threads and pluck away at them with tweezers.