Taylor, Lennard and I also use bearing races to cut patches. Some have a taper into the hole, and need a bit of grinding to sharpen the edges a bit, but they work very well, much better than cutting squares with sizzors. I find when using pre-lubed patches or even spit patches, it is much more convenient to use pre-cuts than stips of cloth. Granted, there is more waste, but not much if done with a plan.
Taylor has a 'round' of spurce in his bacement that his anvil sits on. On the anvil which is a section of 135 pound railway rail inverted and welded to a base he lays his 'race', and sits on a chair faving the anvil. He takes a wide stip of cloth and carefully cuts 5 patches along one seam, scores the cloth and rips off that section the length of the cloth - usually a meter in length. He knows this wide strip of cloth will cut 5 patches per row. It also gives a method of keeping track of the number of patches (if necessary). This way, there is very little waste, done with a bit of care, no more than using a strip of cloth and cutting at the muzzle.
Other methods are with a cutter chucked in a drill press, run at about 1,000rpm - perhaps more. This cuts patches more quickly, and multi-layers can be done, like cutting 20 patches on one pass. Using an arch punch on about 10 layers of cloth, the way I used to cut patches for everything and still do for the .69 when I borrow it back, is also an alternative and with by using the newer 'plastic' (UHMW-HDPE) cutting boards works well. Used to cut patches on a lead sheet, then throw away the bottom patch, every time. Didn't like the idea of sticking the bottom patch in my mouth - OK for pre-lubed, though.
The bearing race and ball bearing is simple, takes up little space to pack and can be easily used at rondy if you run out.