There is lots of information around about respooling 120 onto 620, which might give you some helpful insight.
For reusing your 116 paper, if you're handy with wood, you may want to build some kind of jig to hold the spools and the paper so that everything is contained an controlled while you're working in the dark to tape the film and wind it up.
If you want to get the full length of your roll on the 116 paper, you might consider using 220 instead of 120.
For my 116 box brownie I did the paper negative thing. very easy, though you only get one shot.