I use single point diamond tools on my ultra- precision air bearing lathe to cut Acrylic and other materials giving an OPTICAL finish straight of the lathe.
Single point mono crystalline diamond tools are the way to go- don't use poly crystalline- that gives a bad finish.
I've been polishing glass, germanium and plastic for over 15 years and only ever heard of ionic chemical polishing as an alternative to mechanical polishing or single point diamond turning, but as I recall it was a laborious and costly process.
There's an excellent product for Acrylic polishing called "Magic Polishing Compound" which beats CR39 polishing compound, Cerox and Rouge due to it being in a suspension (less caking and hence less scratches).
I've no connection with the company or biased interest, but would recommend their product unreservedly.
http://www.ceriumoptical.com/Magic.htm