I guess my ultimate stance is this: As I think you agree, a truly Rawlsian universe will never happen. In my opinion, it might even be literally impossible, in sort of a daoist kind of way.

But what I think might be possible, is a Rawlsian justice within a community - potentially at the expense of those not in the community. In other words, we can satisfy Rawlsian justice, as long as we don't commit to the same justice with respect to beings outside the group (i.e. we couldn't meet your condition for "perfectly just" that I highlighted).

We actually already see this to some extend among people, for instance, with certain races or social classes forming little social clubs to help each other out, and keep others down. But my thought is that we should try to expand the Rawlsian community to include all humans - but not including animals, and not including unborn humans.

We could theoretically expand the borders of the community if it becomes feasible - for example, to include cats and dogs, or certain alien lifeforms. But there will always inevitably be a frontier of "souls" or "sentient perspectives" on the outside of the Rawlsian community, that the community simply can't take in without undermining its status as a Rawlsian community.

For instance, if you included cats, maybe you couldn't include mice, because the cats would eat the mice against their will. Unless the mice were genetically altered to be like the waiter in "hitchiker's guide", or the cats were genetically altered not to chase mice or eat meat.

Does that make sense?

I just feel like certain elements of the universe will probably always be at odds with each other, at least for the foreseeable future, forever preventing your truly "perfect" Rawlsian justice. So it seems like the best thing we can do is form enclaves within which, we have a safe haven from those competetive dynamics. But at the very least, we should start by including all humans.