Is there a product opportunity here? Note that saws, at least all saws with toothed blades, cut by chipping the material away, not by slicing through it.
How about a tool like a large tubing or pipe cutter with a utility knife blade rather than a cutting wheel?
Just mark where you want to cut and spin the cutter around the roll a few times for a perfectly clean and accurate cut.
The tool would not have to be large, heavy, and overpowering, it's not cutting steel, just a bit of vinyl. A prototype could probably be fashioned from wood, some casters, a length of threaded rod, and this and that.
Maybe I'll spend my otherwise lazy Sunday afternoon whomping up something.