Even if you could do far better than you are doing now, you still can't do well enough, because you don't please God by being good (Gal. 2:21), but by accepting Jesus (John 1:12).
Sincerity is not the way to heaven. What if you are sincerely wrong? (Remember John 14;6?)
If you are relying on your sincerity, then you are saying because you are sincere, you are therefore good enough, on your own, to be with God. Don't you see, to appeal to your sincerity is to appeal to pride, because you are appealing to something that is in you and not God, for your reason to go to heaven? I am sorry, sincerity is not enough. You must have faith, in Jesus.
How long have you been doing your best? Has it worked so far? Has it given you eternal life?