What kind of cutter are you using?
I made a cutter myself for 127. It's the body of a dead folding camera, and I made a metal plate with a knife-blade mounted on it, which sits in the film gate and cuts the film and the backing paper as I wind it through. I have to wind the cut-down film onto a 127 spool afterwards, in a black bag. I also swithc the film to a backing paper with my own frame-numbers on it. IIRC, for the 4x6cm size I can just about make one set of the existing numbers work, but for the 3x4cm size they overlap in pairs by a little, so it's worth marking my own numbers. For a TLR, I also have to cut the film down for length as well; even if I left more film, the camera won't shoot past frame 12.
There was another complication: with some of my cameras I can get away with keeping the whole length of the 120 film; but then it doesn't fit in my Hewes stainless 127 reel. I can use a Paterson one, but in the end I cut a few mm out of each 'leg' of a 120 reel: I did a terrible job, but it works well enough unless I drop it on the floor.
I put up some photos of my device in the 127 group at flickr:
https://www.flickr.com/photos/century_graphic/albums/72157594255549742
I quite enjoyed all the tinkering this took to get right. The main benefit is being able to use HP5.
Just a thought: if film cut down from 35mm isn't behaving itself, maybe it's stiffer (because thicker) than the 'real' 16mm stuff, and resisting curling up in the takeup side of the cassette? In that case, maybe it would be worth trying cutting from 120.