Your flywheel is 150mm overall? A 140mm AP carbon clutch is 166mm in diameter overall -
http://www.apracing.com/drawings/cp7142cd.pdf
That shows the inner diameter of the clamping area as 97mm.
therefore a 115mm triple plate clutch might be more useful, with the inner diameter being 85mm -
http://www.apracing.com/drawings/cp8153cd.pdf
Hope that helps a bit.