JCL, you'd probably end up like this: agreeing with the IFP on fiscal and foreign policy matters and agreeing with the CPA on social issues. The CPA though isn't completely opposed to your views on economics and foreign policy, they are moderate on both. It's a matter of which views you're willing to compromise.
To cut it short... you're screwed.
Hey man, the IFP is a great party!
That's not really the issue... in order to fit into either party, he'll have to compromise... and JCL is pretty much constitutionally incapable of such a complicated act.