Why should God being Just or Unjust affect ones investigation of Him?
If God exists His standing in this regard is irrelevant. Because God if He does exists has total control over ones eternal destination. If God does exist then one must investigate and find an appropriate response to Him irrespective of how one views Him in regard to His Justice.
It appears that like Enmos, you are missing my brilliant point (!) that what we think about our efforts affects the way we see the goal of our efforts, and that this has an impact on what effort we actually expend.
It is often said that an attitude of "I already know enough, I have already done enough" or an attitude of pride impedes learning.
And I exemplified how such an attitude has self-sabotaging implications for one's search for God.
One can start off with no particular idea about God. But certain ideas about the (in)sufficiency of one's efforts will impact how one goes about one's search and will also color the goal and its worthiness to one.
In short, if one doesn't have certainty about God, but one thinks one has already done enough to come to that certainty, then one will not make further efforts and will view God negatively, thereby seemingly justifying the lack of further effort.