Wolfe, The geometry of the arm actually keeps it vertical constantly and it is very accurate. BUT tapping into plastic... maybe someone else would have insight or give them a call. We use it in steel, aluminum and stainless all day long and it works great.

Tapmatic in the drill press with a work-holding jig is the way to go, we did millions of delicate parts with them. If you had a problem with one it was probably a defective or incorrectly sized unit, they work great. We would also set them up on simple motors and create a moving work-holding piece instead of the drill press.

Len...the ones I've tried were only marginally OK for tapping plastic. Problem was the speed of the drill press and such. More or less "burned" the plastic.
But.. it was also a major hassle to change out every time I needed to drill a hole. Pretty frequent. I tap and drill, tap and drill, tap and drill, tap and drill... I also frequently use the drill press for pushing magnets and steel slugs into fixtures, as a mini-buffer, and other stuff. I even use it as a winder on occasion. The drill press is the most frequently used "multi-use" tool I have.
I'd say it wasted at least an hour a day changing every time I needed to do something other than tap a hole.... that's why I have a dedicated tapper. I tap holes all day long.