Sounds like there are many options to the K/R tool out there. I have been having great success with mine although I've experienced the deadly noose effect you mention.
Two things you can do:
a) avoid wrapping the head too close to the flare of the mandrel, leave a gap and cut the excess like Bill says after by scoring with a razor and snapping apart
It is a little less secure during the tie process but it will prevent the binding effect. The little notch on the body of the tool is supposed to bite into the wall of the tube.
I bought mine from Les Johnson at the Swallows Nest years ago. He showed me the prototype they loaned him which had a machined sharp edge on a harder steel. He said he didn't want to send it back because it bit into the end of the tube much better than the mass produced versions. Over the years, I've realized the wisdom of his observation many times over. In this case that sharp edge is what would hold an oversize tube on a smaller mandrel, preventing compression on the device.