Okay, I know very little about producing a nice finish on delrin.
I've worked with it. Drilling, tapping, milling, etc. The finish wasn't an issue. I probably used a shot of WD-40 just to keep it from squealing. Very easy to machine, taps well. Produces long, stringy chips.
Until a better response comes along, here's a link that might help...
Check out the troubleshooting section.