combination distilling

I want to make an apple-based spirit with the flavor intensity of applejack
but without the headache (methyl alcohol).  Could I freeze distill apple
cider so that the flavor is intensified and then pot distill the applejack
just until the methyl alcohol is gone, keeping what is left in the pot?
Would that be the best of both worlds, or would there be negative side
effects?  Would what's left be cooked and less tasty, or would it be just as
flavorful to distill all of it and just make an apple brandy?

I know it's a strange question.  Thanks for any help.

Vic