I've found here and before that you don't discuss fairly

You're entitled to your opinion, but I'm also entitled to mine, and since we're being open and honest I'll give it. My opinion is that you are not interested in actually understanding the mainstream theories of physics that you are criticizing (and neither is the author of the blog post you linked to); you are only interested in criticizing them.

But you can't honestly criticize a theory that you don't understand; that means that before you criticize a theory, you must be able to explain what it says (even if you think that what it says is wrong) in a way that its own proponents agree to. I haven't yet seen you do this (and the author of the blog post you linked to doesn't either). See further comments below.

Understanding their consequences requires also experimenting with the equations in sufficiently various ways.

I agree with this in principle, but there aren't enough people or enough time to check all the consequences. So it's not a huge achievement just to calculate a new consequence; you need to show that it's significant. See below.

And for the record, I also agree that the model in the blog post correctly applies the equations (although as you and it are using the term "acceleration", it should more properly be "coordinate acceleration"). I just don't agree that this model can explain our observations of redshifts and apparent brightness of distant objects, since its predictions don't match our actual observations of the universe.

Apparently that wasn't done until the blog author did it, or else I'd likely be able to do a Google search to find elsewhere that acceleration away can be shown by those equations.

Okay, let's assume you're right that nobody has ever done the precise calculations that the blog post's author did, before he did them. If you had said just that--that mainstream physics has never considered the calculation the blog post author did before--I might still have been a bit skeptical, but I probably would have let it pass. Your claim came across as a stronger claim than that; you appeared to be claiming that, if you showed the blog post's calculation to a mainstream physicist, they would say it was wrong--not wrong as in not applicable to the expansion of the universe, but wrong as in incorrectly calculating the consequences of the relativistic rocket equation.

I strongly doubt that is the case, since, as I said above, I agree that the blog post author has calculated the correct numbers using the relativistic rocket equation (even though I don't agree with his application of those numbers to a different scenario). I strongly suspect that if you showed the blog post calculations to a physicist familiar with relativity (such as the author of the relativistic rocket equation page in the Usenet Physics FAQ, which the blog post links to), they would react the way I did: yes, this is a correct calculation using the relativistic rocket equation, but it's not relevant to the expansion of the universe. So saying that "generally accepted physics doesn't recognize that an unpowered projectile launched upward can accelerate away" does not, I think, describe what mainstream physics says in a way that a mainstream physicist would agree to.