Okay, some high flow resistance paper is in my future...

It would be interesting to try this in a 'layer cake' three-paper stack: Filter paper shot forensics

My initial guess is that it will go badly, since the 2.5um paper will have a significantly higher flow resistance than the coffee grounds. On the other hand, the AeroPress paper I've been using mid-puck is largely transparent to the flow resistance - but seems very effective at stopping top-to-bottom channels from forming.

ohwhen wrote:I think it would be slightly more cumbersome than a punch cutter but you can also look for "circle cutters" that are adjustable.

I picked up one of these since the ability to change sizes was appealing, plus they are more compact, easier to store, slightly less expensive, and have replaceable blades.
Would not recommend:
1. Fiddly
2. Leaves a hole in the middle of the paper (and to avoid the hole makes the cut more challenging)
3. Slow
4. Not easy to do more than two filters at once

I ordered a pack of the Aieve papers on Amazon. They seem to be the generic ones that are sold under a few names. I've compare them with the Aeropress filters once I get them on Monday.