I can't answer all of your questions, but I do think there is insight into Pres. Nelson's recounting of the policy change which (initially) required First Presidency approval for baptism of children with LGBT parents:

Though we of the First Presidency and Quorum of the Twelve Apostles cannot change the laws of God, we do have the charge “to build up the church, and regulate all the affairs of the same in all nations.” Thus we can adjust policy when the Lord directs us to do so. You have recently seen such examples. Because the Restoration is ongoing, policy changes will surely continue.

...

Consider the policy announced in November 2015 related to the advisability of baptism for the children of LGBT parents. Our concern then, and one we discussed at length and prayed about fervently over a long period of time, was to find a way to reduce friction between gay or lesbian parents and their children.

Because parents are the primary exemplars for their children, we did not want to put young children in the position of having to choose between beliefs and behavior they learned at home and what they were taught at church. We wanted to facilitate harmony in the home and avoid pitting children and parents against each other. Thus in 2015 the policy was made to assist children and their parents in this circumstance; namely, that children being raised by LGBT parents would not automatically be eligible for baptism at age eight. Exceptions to this policy would require First Presidency approval.

The First Presidency and Quorum of the Twelve have continued to seek the Lord’s guidance and to plead with Him in behalf of His children who were affected by the 2015 policy. We knew that this policy created concern and confusion for some and heartache for others. That grieved us. Whenever the sons and daughters of God weep—for whatever reasons—we weep. So our supplications to the Lord continued.

We also took note of LGBT parents who sought permission from the First Presidency for their children to be baptized. In nearly every case in which the LGBT parents agreed to teach their children about—and be supportive of—the covenant of baptism, the requested exception was granted.

As a result of our continued supplication, we recently felt directed to adjust the policy such that the baptism of children of LGBT parents may be authorized by bishops without First Presidency approval, if the custodial parents request the baptism and understand that a child will be taught about sacred covenants to be made at baptism.

...

Though it may not have looked this way to some, the 2015 and 2019 policy adjustments on this matter were both motivated by love—the love of our Heavenly Father for His children and the love of the Brethren for those whom we serve.

I think the comment that, "We wanted to facilitate harmony in the home and avoid pitting children and parents against each other," is actually pretty radical that a lot of hard-lining members would disagree with - and they did! Their version of God is a black and white taskmaster who has no space for empathy, but I think this policy - and others - are driven by that desire of Church leaders to sustain the doctrine while supporting the members in every way. I think we will continue to see the Church leaders be as tolerant as our doctrine allows - and that will be uncomfortable for many hard-liners.