Thanks to my new book I just got in the mail I finally figured out my problem with 3D to 2D projection.
I was on the right track but just couldn't sort it out.
p=[p1,p2,p3,1][IM]=[p1,p2,p3,p3] or p', for p3!=0
This is vector in homogenous space - to map it back to three dimensions divide each component by w.
Pretty simple really, dunno why I couldn't derive it.