In a puzzle like 630, rather than freezing the loops between sheets and putting cuts where they meet the sheets, it might be better to leave the loop residues unfrozen and put the cut in the middle of the loop, so that the cut has a couple of unfrozen residues on either side of it. This will allow cuts to close better.
This wasn't clear enough in the puzzle description but you don't need to close the cutpoints on this puzzle.
In fact, you cannot close the cutpoints even if you tried!
I have changed this to ALL CAPS in the puzzle description.
It will allow the cuts to pull together without moving the parts you've just positioned.
we need local wiggle also to move the loops