I once thought I had experienced this, but it could be just my psychology making up these experiences couldn't it?
Anything is possible.
Do you mean responses to prayer here or things like the resurrection? I used to think reasoned arguments like the Kalam cosmological argument and fine-tuning were good arguments. The problem is that reasoned arguments like this rely on perfect reasoning abilities.
I would say things like the Bible. Koran, Vedas etc. are eyewitness testimony but there are other testimonies as well from other quarters. Reasoned arguments can lead one to belief but can also lead one to non belief. Everything depends on one's initial assumptions. People's initial assumptions differ so reasoning is not an effective way to change people's beliefs as you end up arguing facts that you perceive from different angles and through different lenses.
I wouldn't say they consciously believe for these reasons.
I would hesitate to ascribe sub conscious reasons to anyone.
But a future medical breakthrough doesn't assure you of eternal life, whereas God does.
I don't think that the existence of God necessarily assures eternal life for anyone other than God.
If there were a God I doubt that morality is moral because God wills it, rather that God wills it because it is moral
How did God find out it was moral? If God is the first cause and creator, which is the way we seem to be defining Him in this thread, then how could morality not be a creation of God and entirely subjective by Him? You must assume another agency is at work if God is constrained from deciding what He will call moral but must acquiesce in calling something moral because it is that by nature and not by any design of His.