Howdy bud

Out of Acrylic and Polycarbonate, Acrylic is going to be your best bet. Polycarbonate is an engineering plastic. It can be machined more easily than Acrylic but it will also scratch more readily. I'm not really surprised you are having trouble finding black polycarb, I have not seen any on my travels but I also think you should avoid it for the reason above.
Have you thought about building up layers of plastics? I am making something at the moment with a solid white acrylic center with clear outer acrylic layers which should look pretty nice, I imagine something in black would look pretty hawt too. This of course would be a gloss finish and maybe not what you are after.
Another other option would be to make something and then case/laminate it in/with a plastic. I.e you could have a MDF core and then cover it in Delrin or [
Acetel] etc to keep the cost down.
[
HIPs] is VERY reasonably priced and I know some forum members have used it, SpacedHedgehog used it on his Vewlix cabinet. I keep meaning to get some samples to have a play with but as usual I have about a brazillion things on the go.