Installing cushion vinyl over carpet
You're right, not the best way to do this. The vinyl will shrink a bit when cut if not glued down so don't try to cut it to fit. I'd keep at least an inch so you can trim to fit as you already know how hard it is to trim it accurately.

Using the carpet as a template won't work either because carpet edges are never cut to fit exactly. Their edges are stuffed down between the walls and tack strips. I'd wait until you're ready for the final installation and then get some construction paper and make an exact template by laying out the paper in the hallway and taping it all together. then lay the template over your sheet vinyl and cut with a straight edge and utility knife.