I wrapped a length of about 10 ft onto 2 pieces of broom handle that I cut. Makes it easier on the fingers.

Also, keep it as flat as possible, avoid the edges of the badges and use long, fast strokes (not those strokes, Mayfair). About 1 ft of fishing line, using the whole length worked really good.

That seemed to cut right through the tape like butter.

 

I'll give it another go this weekend.