I got the threads cut and pulled today. The trick is to only cut threads perpendicular to the ends of the kloster blocks, NOT parallel to the sides of the kloster blocks.
It used to be really scary to cut into my stitching but now that I know what I'm doing, it's not scary at all. Once the threads are removed, there are open squares and cross-crossing grids of 4 threads.
The instructions state to wrap pairs of threads, then do the dove's eyes. I wasn't really happy with the result. My dove's eyes were a little 'wonky' because I didn't feel they were anchored/centred enough.
So on the other half, I wove pairs of threads together. That gave me something on which I could centre the dove's eyes. They were much more consistent that way. On my 'real' piece I'm going to use this technique.