This is interesting.
As far as I'm concerned, I see the Beyonders as the corrispective of the Monitors, i.e. the highest "beings" in their respective sphere of existence.
Monitors are direct creations of the white page itself, they watch (more correctly, watched) over the whole DCU which they consider to be an interesting can of germs, they can stop time in the whole DCU and prevent it to go any further as story, and, finally, they are the only ones who can manipulate the bleed, which is the essence, the blood of the story itself.
Yet despite being this kind of hypergods (as Morrison called them), they studied the CA for eons but still they barely managed to understand what it was, let alone how it has been made.
This is because the CA is basically half of the very original, limitless probe, part of the white page itself (PM), which mapped and blended with the whole existence at the beginning of times.
This description should make clear how exponentially high the CA is in the whole DCU hierarchy (basically it is at the very top), that's why I still put my money on the CA here.
Still, I understand how also big the concept of the Beyonders is, so I surely won't be scandalized if someone votes for them.
The difference between Monitors and Beyonders is that the former accumulated quite a few less-than-stellar feats(to say the least) during Countdown.
As for Thought-Robot:
It was constructed by Dax Novu(one of the original 'Probes' created by the Primal Monitor itself) as the ultimate weapon of 'good' to be used against the ultimate weapon of 'evil'.
Basically, after Dax Novu first encountered the concept of 'story' within the multiverse, he knew that it(ie. story) would ultimately consume him--he knew that he would eventually become Mandrakk: the 'evil' aspect of story on a fundamental level. To combat the threat he would one day become, Dax built a living armor based on the most powerful aspect of a 'good' story he had encountered whilst probing the multiverse: Thought-Robot(built specifically for Superman's story.) In a nutshell: Dax built a plot-device against himself.
Despite this, Thought-Robot only 'beat' the first iteration of Mandrakk by throwing him into the Overvoid--the mind of Primal Monitor. Here, the very idea of Mandrakk was nullified/lost. We then learned that Rox Ogama had inherited the throne of Mandrakk, and despite being less powerful than his original counterpart, he was still considerably above most other 3-dimensional forces. He was only beaten when Superman used the Miracle Machine to wish for a "happy ending." Nix Uotan(Rox Ogama's son, who was acting in his full capacity as a multiversal Monitor at the time) received/interpreted Superman's wish from his higher-dimensional vantage point, and assembled the forces necessary to destroy Mandrakk II once and for all: the Supermen of the multiverse, the Pax Dei, the Zoo Crew, the Forever People of the 5th World, the GLC, etc.
Afterward, the multiverse itself was restored/rebooted.
Anyway, that's just my interpretation of the events. Good to have multiple viewpoints on a story this complex.
Your interpretation of the book is basically just like mine, really.
I said in my previous post that the CA is half of the orignal probe because, from what I understand from the lecture, it generated (through the oringal probe itself's powers) when said original non-dual probe, corrupted by duality of reality, split in two: one part was Dax Novu, the probe itself, took over by the evil concept of Mandrakk (evil part of the page which devours stories), while the other part was the CA, the last gift of Dax itself before corruption, which is the story/concept of Superman (the most powerful and important idea in the DCU bar none) shaped as a doomsday weapon.
Then, the opposites fought on the edge of the white page, outside of story (story which is the DCU).
What is life, space and time inside the DCU for every character, from the perspective of Mandrakk and the CA is nothing but a story: Mandrakk wants to erase it until only the white page (PM) is left, while the CA's purpose is to save and protect it.
At the end of the day, every plane of existence of the DCU is just so insignificant and inconsequential if compared to Dax/CA that it's really mindblowing: I personally like to think to the PM/Dax/CA concept like the equivalent of the God/Lucifer/Michael relationship, just, to me, on a higher scale such as a metaversal level: this limitless non dual essence that is the PM which is infinitely bigger than the all of creation, its probe, that part of itself which wants to erase stories, the biggest and most powerful story of all (in DC) somehow shaped as a doomsday weapon, which, bigger than creation as well, awaits for eons at the verge of the page for the final clash which will determine if the story (DCU) will go on or if it will cease to exist...
All of that is just immense to me: I had to read the story two or three times in order to grasp every detail and in order to have everything flow, but it really was worth it; never read anything which left me impressed and gave me the idea of the word "powerful" like that, really.
You are right: no version of Superman can win here, not Silver age with SoS nor Prime One Million or Quantum Superman.
Anyway, the CA is not a version of Superman, it is the idea which led to the creation of the story of Superman somehow shaped as doomsday weapon.
The CA isn't Superman.