Polished acrylic machining

Let's say I wanted to do some Taig CNC milling on an acrylic or
polycarbonate block. The result needs to have some decent optical
clarity but I expect the tooling will result in a fairly scratched,
milky surface.

Is there any simple answer for this? I know there are plastic polishes
that can kinda buff that out but I'd expect major problems getting a
Dremel buffer wheel into small low spots. Is there any magic cutting
head or something that results in a smooth surface, or some special tool
or chemical for removing them?

Thanks