Help trying to make a 16-bit pixel effect

I'm trying to make some animations for a retro style video game and I had the bright idea to just record myself doing the animations, pixelate them and extract the frames. I've watched a few tutorials and I've tried messing around with the mossaic and posturize effects. The general idea is there, but it looks pretty terrible. 

I think the biggest problem is the way it blurs the colours together and tends to pick a bland "middle" colour. For example blue jeans are mostly slightly bluish grey, as its a mix of the different shades of blue that exist in that space.

I'm thinking the answer is probably just going to be that I need to actually put in the time and effort to do this properly, but is there any way to set a palette of selected colours, so the posturize effect will choose the closest of the acceptable options? 

Or does anyone have a suggestion of how I can get this effect my other means?