Where should I begin looking?

There are major differences between the two, since one must follow scientific/natural laws and the other not, but I drew my conclusion based on trends that I saw. One, just as a for instance, is the idea that slavery is okay. It used to be a practically universal policy that worked well in its time. But as countries developed, they began seeing moral issues with it, and it had a challenge. When put under the new pressure of people who disagreed taking action, it started to fade. Its not gone in the modern world, I am somewhat sure it goes on under the table or in other less developed/less looked at countries, but in a vaster majority of the world it has fallen away and been made illegal and unacceptable. It worked at then time but mean pressures made it not feasible in a sense any more and now its widely gone. It is changes like that in thinking and policy that lead me to that conclusion that societal and biological evolution are comparable.
I think that your conclusion that societal and biological evolution are comparable, is correct. And in the timeline of modern history and in broad generalities, I agree that societal mores and actions are becoming progressively humanistic. Where I disagree is with the implicit assumption that this is an inevitably continuing course. Conditions change. In biological evolution, if conditions change drastically enough, the traits that survive and become pronounced in organisms may be ones that were common in past generations or they may be something new (but still a product, in part, of the newly existing conditions). Comparably, societal mores and actions are a product of existing conditions. My contention is that we cannot, reasonably, expect conditions to perpetually promote an increasingly progressive humanistic societal bent. OTOH, to the extent that societies can remain intact and build on the best of what has been retained, your belief (#4) may be, and I hope is, essentially, correct.
My contention is that we cannot, reasonably, expect conditions to perpetually promote an increasingly progressive humanistic societal bent.
I agree completely. In fact I see more cases in which humanistic and progressive ideologies can be countered and impeded by changing conditions. While I see these ideas as beneficial and correct, they are not the end goal of societal evolution, and are subject to suppression by the same things that made slavery suppressed. While I think its beneficial that shouldn't be conflated with whether or not it is always fit to expand or thrive as an ideology in a given place/set of conditions. That is another way in which I find societal and biological evolution to be similar.
There are major differences between the two, since one must follow scientific/natural laws and the other not...
I am nitpicking here (not to be contentious, but rather as a vehicle for sharing a bit of my particular "book"): From my perspective, both follow scientific/natural laws, just a different set (in some important aspects) of scientific/natural laws). Speaking in broad, terse generalities, I think that one follows Darwinian principles, while the other follows laws of behavior identified by Skinner (which incorporates Darwinian principles and expounds on the behavior of organisms). (This is my particular lens.)
My contention is that we cannot, reasonably, expect conditions to perpetually promote an increasingly progressive humanistic societal bent.
I agree completely. In fact I see more cases in which humanistic and progressive ideologies can be countered and impeded by changing conditions. While I see these ideas as beneficial and correct, they are not the end goal of societal evolution, and are subject to suppression by the same things that made slavery suppressed. While I think its beneficial that shouldn't be conflated with whether or not it is always fit to expand or thrive as an ideology in a given place/set of conditions. That is another way in which I find societal and biological evolution to be similar. True. And with that insight, I think that it is valuable to, also, understand how the underlying mechanisms of the two processes are different.
That is my issue, atheism describes one thing that I don't believe, and nothing of what I do believe, so although it can be useful it has extreme limits on what it says about me.
Is there any term in the English language that tells all about you? I can't think of one that tells all about me. It would take several, at least. I'm an atheist and I sometimes describe myself that way. I am also a Humanist and sometimes describe myself that way. But neither nor both terms describe me fully. Every term I can think of leaves out something important. Words can only describe some aspect of us. I can't think of one or even five that describe me fully. I use the term that fits the occasion and assume that intelligent people will know that I don't mean it to define me. Less intelligent people can be dismissed. Lois

My thankfulness & appreciation .

Well, I think you can stop your searching. Your list pretty much sums up a great philosophy of life shared, I believe, by many here. Perhaps you can focus on the lightening up part. Repeat to yourself: A little song, a little dance, a little seltzer down the pants.
Don't forget to smell the roses!
To play off of your analogy, its like I am simultaneously writing each chapter of the untitled book of who I am, adding to each as I go along. But there is no order to them, its a work in progress and I guess I want organization in it, but maybe its naive to suspect that I can take a malleable changing item and give it lasting order.
Striving to catch the Whirling Dervishes dancing through your life/mind, we are? {in my best Yoda} ;-)