Help me out, r/atheism: Christianity, heaven and the problem of free will.

I've entered into a few discussions with Christians who insist that God created us with free will, and that free will is why we sin and must actively seek redemption. One of the things that bothered me about this argument finally coalesced: heaven and a world without sin.

In the Bible, God creates Adam and Eve without sin, but the capacity for it if they choose. This, according to standard Christian dogma, is the problem of free will. Once Adam and Eve sinned, we were all infected with it so we're prone to sin from birth. Only God's sacrifice of Jesus on the Cross provides a means for us to escape the consequences of sin, but won't stop us from committing it.

Then, also according to the Bible and standard Christian dogma, after Armageddon God will destroy Heaven and Earth to make way for a new paradise where everyone who accepted Christ as their savior will live in eternal bliss -- a world without sin.

I'm not quite sure how this jives. God originally created us with the capacity for sin because of free will. Yet, once his Divine Plan is complete the blessed will be free of sin, and theoretically without free will. Or if they do have free will, it won't carry the possibility of sin. So why wouldn't a perfect, omnipotent and omniscient God have set things up this way in the first place?

Please tear this apart and tell me the weaknesses in my analysis.