Thanks Wokka, yeah I'm not worried about the bleed in places, I knew I'd end up needing to scrape a bit and the amount is my fault for not taking more care with the tape.
I was thinking of making a scraper out of a bit of dowel and a stanley knife blade. Cut a slot in the top of the dowel, wedge the blade in to the right depth, secure with a bolt and wing nut.
Here's a terrible MS Paint rendition:
My theory is that it'll be impossible to go too far with this, since any rotation of the dowel will just shorten the blade in relation to the binding.
Alternatively, I could just be really careful...