Ok, to get started we should talk about the parts I bought. A lot of the design decisions were based, not surprisingly, on what I had in stock. Bearing choices, linear shafts, the aluminum base, were all stock materials.
Let's get right to it.
Most important is the blades. I originally tried to do it with standard utility knife blades, but that ended up tearing the paper after a remarkably short time, so spinning blades were the better option. Specifically these (fabric cutter blades):

(representation only, not actual blade below)
To spin these blades I first tried a small brushed motor, but it just didn't have the torque necessary. So I went to a BLDC outrunner which, at basically the same diameter and half the length, has far more torque.
Of course the downside to BLDC is you need a driver, and that is a remarkably deep subject, but for our purposes a little off the shelf driver will do. This one comes with a speed potentiometer
For some weird reason I spun my own stepper driver board with an ESP32 (Wemos D1 Mini) and one of these (or similar) little off the shelf stepper drivers, but you can just get any stepper driver mechanism that will allow you to vary the feed rate.
Now, for the bad news. You might need a lathe to complete this project. Almost all of the parts you can make with standard tools, but there is one that will likely require some imagination.
The paper reels, after they are cut, need to be removable from the machine all rolled up on their axles.
That means the whole axle assembly needs to be quick-release. So there's a little lever that holds the shaft in place
That whole assembly is held into the stepper by a little coupler thingie that involves, I think, old bowden tube from a 3D printer
That's the part that would require a Lathe, though I think you could do it purely native 3D printed with some heat-set inserts.
More to come...