I don't see any scriptural reference to God hearing the "insincere"... The Lord does not heed to the beck and call of the pagan. Yes, the Lord "hears" all things, as he's omnipotent, but he doesn't "HEED" to all prayers. And he turns a deaf ear. There are several scriptures that reference that God does not like LIP SERVICE and this is in reference to the brethren. There will be a lot of "saved" people who will go before the Lord on judgement day and say, "Lord, Lord, did we not prophesy in thy name and do all these wonderful things..etc. etc."... And the Lord says in return, "Depart from me, I knew you not..."
This is an example of LIP SERVICE and not HEART SERVICE. God is not a special Jeannie that we rub and summon with special words and meaningless repetitive (unheartfelt) dialog. This type of activity is actually occultic.
Approach the Lord with a sincere heart and cast all your cares upon his feet. Also, be very careful of who you share your "secrets" with. Take your prayers to the closet if you must.