1 Timothy 2:14 And Adam was not deceived, but the woman being deceived was in the transgression.
If we back up and take a look at the book of Timothy thus far, it starts out with the purpose of rejecting false doctrines that do not conform to the gospel or life of Christ. Basically Paul is calling out what is wrong. He then goes into a reflection where he recalls all the wrong he had done prior to his conversion as he recounts how he was a vile and cruel man. If we want to get in Paul's head, I'm sure he's remembering the stoning of Stephen in Acts 7. But what does Paul say on the matter except that he was shown mercy as an example to those who would be saved. In essence, Paul is saying if God can save me, he can save anyone... including those who are preaching false doctrines.
During this discourse, Paul states emphatically that he committed his crimes against God and Humanity in "ignorance and disbelief". If we look at the book of Numbers 15:22-36 we see how sins committed in ignorance are handled. We also see how somebody who is defiant is treated. This is in agreement with what Jesus stated in Matthew 18:15-17.
As a side note: When Jesus was on the cross what did he say? "Father forgive them, for they know not what they do". And what did Stephen say when he was being stoned? “Lord, do not hold this sin against them.” Why? Because as Paul stated, he was ignorant and as Peter said in Acts 3:17 I know that you acted in ignorance, as did your leaders...
So very clearly we see that when Paul bring up Hymenaeus and Alexander, it is clear that these two who are preaching false doctrines are doing so defiantly, and not out of ignorance. Lets be very clear as Paul states. There is a difference between being ignorant and being defiant. This is why Paul says that their faith has become shipwrecked.
As with Stephen, Paul then goes into prayer and why we should pray and this brings us to Women in the church and more to your point, Adam and Eve.
3 For Adam was formed first, then Eve. 14 And Adam was not the one deceived; it was the woman who was deceived and became a sinner.
If Adam was not deceived, then he acted in defiant disobedience. Thus, Adam and Eve were "Cast out" of the garden. Cast out of perfect fellowship with God.
Does this get us moving in the right direction?