How old is it? I've had my Phantom 4 years now (I think) and it has definitely become smoother as it has broken in.
The last thing I can think of that might be causing you trouble is the smoothness of the pump handle on the pump rod. I had a Wevo undercocking kit (same as the CCI kit) that was a bit rough and ended up taking some fine sand paper to smooth out the inside of the pump arm. Try taking the pump kit off the marker and seeing how smooth the handle moves on the mounting block. If you feel it chattering a bit, you might be able to smooth that out.
Other than that, and the rest of the advice in this thread, you could keep using your phantom and breaking it in, or maybe move on to another marker that known to have a smoother pump stroke (ie a Carter machine, a Retro 7, a Sniper, or a Sterling).