Have you tried to hold down SHIFT and click on all the tracks or blue takes you want to copy, then select the puppet in the other scene and paste that? I think you can also draw out a rectangle to select lots of things at once. You can also duplicate a whole scene and then delete/edit it afterwards.
I am not sure how much copy/paste works these days. It used to be not much worked, but they added a lot more support in recent releases (including some support for pasting into a different puppet - if similar enough structure). (Sorry, not at a computer right now to try it.)