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Nice idea and noble aim in principle, but a flawed question to be asking.
Your main problem lies - and this is the main criticism of living by the Golden Rule - with the fact that what someone regards as "most benevolently righteous" will vary from person to person and place to place. Ergo you can conclude that such a thing would be impossible. Even if you satisfied a majority, you'd still dissatisfy a minority - or even actively oppress a minority! There is no way to objectively say what would form a righteous and benevolent government because the criteria that you use to assess it are still ultimately subjective. For instance, would you prefer a society where one person has a happiness of 10 and another has a happiness of 1 (arbitrary scales for illustration purposes) or a society where two people both have a happiness of 3. There are arguments in favour of both but no true test showing which is actually better. Thus one person may prefer the former and another the latter. Someone is going to be disappointed and not view your regime as benevolent or righteous.
Your only practical solution to this would be to split society into increasingly smaller groups whereby everyone in a group has a similar view and is governed only by the laws they view as benevolent. Eventually this would reduce everyone to living in a society of one, probably simulated to their idea of utopia. However, with the lack of conflict or friction, the desire to strive and improve is removed. Such a place may not be the most desirable place to live because it would remove this key aspect of human motivation. Indeed, going by the relativity of the definitions and the varied opinions involved, a regime that is the "most" benevolent and righteous might not be considered as the most benevolent and righteous.
But the question asked the most "benevolently righteous regime possible", not the most benevolent regime period. The most benevolently righteous regime possible (MBRRP) would necessarily be a compromise between differing notions about its nature, I think.
The "most benevolent regime period" is practically synonymous with "the most benevolent regime possible" - the key is in the "most" part, implying that we can only get so far in either case.
Regardless, you would still have to define not only benevolence and righteousness by subjective criteria but also how you're going to measure it. Even saying "the regime that most people think is most benevolent" still isn't objectively the best criteria to judge it by. Certainly that minority who didn't agree about the level of benevolence would complain about using a majority vote as a measure. Take the UK election system. The Liberal Democrats want to change to a proportional system because if you define it like this it's the best. Tories want to keep it as is, because if you define it like that it's the best. Even merely saying "compromise" can be tricky, because you run the risk of diluting the ideas down so far that they can't be properly executed and are ineffective. Such a compromise idea between all opinions would lead a system that pleased no one because everything that an individual wanted would be stopped short by another persons wants and needs. We see such examples all the time where proposed laws are compromised on and weakened, and we end up with final drafts that no one particularly wants. The law doesn't go far enough for its supporters and goes too far for its opponents - despite shining public faces of "well, we made a good compromise so it's all great" everyone, deep down, is actually unhappy about it.
I you imagine "most" as the maximum on a curve, then it's easy to find where you want to be for any particular system, regime or otherwise. However, because of choosing your definitions by subjective criteria, and these change between people, there isn't just one curve but several, and their maxima are found in different locations. A compromise situation would end up with a curve with no maxima, but a mere straight and flat line, probably very low down.
And that's without getting into specifics about defining a benevolent act. In one particular model, if you want to define "most benevolent" as just reducing harmful acts to an absolute minimum, then the "most benevolent regime" would, in fact, be no regime at all - as something that can't exist cannot be malevolent in any way.
We let the super-intelligent "Minds" decide how to execute policy, with the possible exception of going to war. As to what policy should be, yes, there will always be disagreement, but ideally the mantra would be "if you think you'd be better off in a different system, don't interfere with those who don't, or go elsewhere."
Both of these would only be optimal or even possible in a society that lacked serious cultural/moral heterogeneity and had done away with money, poverty, illness... I think perhaps you're thinking more about the here and now, when I'm thinking more abstractly about the (distant) future.
(I think my point is far more abstract that you seem to think it is!)
Which God decided that "intelligence" (regardless of how high) is a required criteria for deciding benevolence? Would they have a better idea about how someone would want to be treated than that person themselves, for instance. Again, it's all basing it on ultimately arbitrary criteria.
I would think it would be more like this: each individual who opts to live in this "benevolent regime" would essentially decide however to live their own life, under the guiding principle that "my right to swing my fist ends where the other man's face begins." Ultimately you can't make everyone happy, so those who simply cannot abide this regime would be forced to leave it.
These criteria are arbitrary. It's arbitrarily an anarchist-communist utopia based on hedonism. However, I believe that under that arbitrary system the most benevolently righteous regime would be able to function, i.e., that is the best form of society.
I can't justify this point of view scientifically or logically, because doing so would require too many a priori assumptions. Why is intelligence necessary to make good policy? I suppose you could get lucky, but that's not a government I would put much faith in.
Oop, my bad. I meant the most benevolently righteous regime that actually exists in the world today. I shall update it. I always seem to screw things up this way.
"However, with the lack of conflict or friction, the desire to strive and improve is removed" They could ask others to give them such and/or ask the system to limit their powers, including modifying their memories that they have done so, so that they can conflict and strive in a number of virtual worlds all they like.
With "equal omnipotence" there is still politics. There is no longer any physical limitation, so physics becomes a realm of artwork and social games.
But there are also mental/psychological limitations. There may be limitless frontiers due to the difficulty with acquiring knowledge without inducing suffering. The knowledge is required to know what we would want to do, how to improve our mind and experience. This may be a never ending process of discovery. No matter how good we become, we could always be better.