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) and trusting in what He did on the cross--not what you do by your own effort.
Sincerity is not the way to Heaven. What if you are sincerely wrong? (Remember John 14:6 says salvation is through Jesus, not sincerity).
If you are relying on your sincerity, then you are saying that because you are sincere that you are, therefore, good enough on your own to be with God. Don't you see that to appeal to your sincerity is to appeal to your own goodness which is ultimately an appeal to pride. This is 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?