I think it could be as simple as rewarding for lowest number of cuts. Don’t have to explicitly disallow, just encourage in the direction you want.
Honestly it’s quite fun doing the cheesy way, but if I had something at the end of the level saying how few cuts I used or maybe even out of 3 stars I achieved for how few, then I’d do it; have fun; then try again.
That to say I think that it’s a great game and I hope to see a post jam version!