What is the role of human judgement given God's omnipotence and his plans For example, some people view evangelism to be "most effective" using one method, whislt another person might view it as "most effective" to use another method. Ie, our opinions (and hence actions) can bring us closer/further away from God.

Another example would be differing views of the interpretation of the bible. Our opinions can be correct and hence bring us closer to God, or they can be incorrect and take us away from him.

To what extent can we rely on our own human judgement to help build a better relationship with God?
Actually this is a very good question.
The first thing to realize is that relationship is a two-way street.

When someone became a Christian, he or she began with accepting Christ. That's no work on our part, we just receive the Gift of Salvation.

Afterwards, the Holy Spirit is now living inside of this believer, preparing him or her to become God's temple. This is the critical point when the relationship between this believer and God began.  Two outcomes can result:


If the believer undergoes discipleship (as the Lord commanded in Matthew 28:19) that points him in the direction of submission to the authority of the Scripture and the Holy Spirit and he took the time to consume the Bible regularly without being critical, he will grow closer to God as the result. Which makes his judgement no longer relies on his own wisdom or intellects, but rather it will be more and more influenced by God's will in this person's life.
If the believer got stuck or distracted in the various ways (lack of discipleship, "instant-sunday-school"-recruitment, extreme dependence on liturgies, doctrinal debates, guilt-driven social works, became a celebrity, you name it). He remains distant from God and never acquire that growing relationship, because he is too busy doing his Christian actions rather than immerse himself in the Scriptures. Or he is so critical in his Bible reading.  In this case, his judgement is not Godly, is still of himself, and not only being useless for himself, but can also mislead others.


Therefore you see, our (human or self) judgement does not propel us closer to God by itself, only the Holy Spirit can do that.
Only when we submit to His authority, we can start reading the Bible with the right attitude, which will cause our judgement to be more God-powered, and less self-powered.

Last thought: God's plan is designed to be executed by God-powered Christians. It was not meant to be shouldered by self-powered individuals.

Hope this helps. And thank you for the excellent question.