Two months of no real progress on the game, but: I've got a CNC router!
It's... currently sitting on top of the bed in my spare bedroom, because I horribly underestimated how big it would be. But that's fine, not many guests during COVID. I haven't done any really big serious work with it yet, but it seems to work fine for my small tests I've run so far, so I don't think anything should change much.
I did some test cuts using a straight edged router bit (not sure the correct term for this), which was recommended for cutting plastics (since it doesn't have a helix to pull up the material). With a spare bit of lexan, it didn't do too well, sorta ripping up the edges and melting them a bit, similar to the issues I had cutting my lexan by hand with a drill. I got a sheet of 1/16" acrylic and tried that, and it cut much better. Not perfect, but definitely presentable. The only issue is that acrylic has a tendency to crack and shatter randomly. The router bit hasn't caused any of that yet, but when doing a whole playfield it could potentially cause an issue. I also tried another scrap of plastic I had on hand (which I think is PET-G, but I didn't label it), and it cut super nice. I'm trying to source some PET-G sheets locally to test out but I haven't found anything so far, so I'm gonna go ahead and try the thicker acrylic first. Acrylic also is (supposedly) what 70s+80s games with plastic playfields used, and what other homebrews have, so I'm still hopeful it'll work.