I agree that we should not take Jesus’ blanket prohibition against making judgments literally. Otherwise Jesus is being illogical, for simply to place not judging above judging is a judgment. So I understand Jesus to be arguing against becoming judgmental.
Jesus’ teaching should be compared to those of his rabbinic colleagues. The rabbis taught, “Judge all people by their deeds,” (Pirke Avot I:6). Judging a people according to the quality of their actions provides a sound foundation for good judgment, and avoids playing God and trying to judge a person’s heart. The rabbis also taught, “Those who judge according to deeds will in turn be judged according to deeds,” (Shabbat, 127b). While the rabbis believe “God desires the heart,” (Sefer Hasidim, 5-6) it is the quality of one’s actions that determines one’s fate because actions are controllable while feelings or thoughts arise of their own accord. Lastly we can see parallels to Jesus’ log and speck analogy in the rabbinic teaching, “Those who condemn others see in them their own faults,” (Kiddushin, 70a).
One question I would raise regarding these teachings of Jesus is whether or not he himself lived up to them. Clearly he did not. Jesus not only judges, he is often judgmental. To cite only one example, Jesus regularly calls people hypocrites. The word occurs only once in the entire Hebrew Bible (Psalm 26:4 NRSV) and twelve times in the Gospel According to Matthew (6:2; 6:5; 6:16; 15:7; 22:18; 23:13; 23:15; 23:23; 23:25; 23:27; 23:29; and 24:51 NRSV)! I have no problem forgiving Jesus his log, and in fact it makes him all the more human and accessible, but it is still important to note that he himself had work.
Regarding personal log removal, I think I understand what you are saying about the Holy Spirit, though I prefer to place my faith in trusted friends and a good therapist. When it comes to helping me see the log in my own eye, I suspect that the Holy Spirit is often my ego in Holy Spirit clothing excusing the log and exaggerating the other person’s speck.
My last comment speaks to your notion that “we're no longer out to remake the world and others into our own image!” I know what you mean, and I don’t disagree, but in the interest of creative dialogue let me suggest that when we realize our true image, meaning God in whose image we are made, we are indeed out to remake the world in our/God's image. The entire Jewish enterprise is one of tikkun hanefesh tikkun haolam, reclaiming the image of God in our souls that we might remake the world in that image as well, applying justice and compassion as best we can on every level of human interaction (personal, interpersonal, and transpersonal), as well as in our interactions with other species and nature as a whole.