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Edwin,
I agree we necessarily need to focus on those areas which we have a reasonable grasp, which is why I'm not commenting on the body of your work. I only raise the issue because I do strongly feel that the Big Bang model is slowly crumbling and only continues due to the willingness of the cosmology community to accept increasingly fantastical patches in order to avoid having to admit the holes they cover are far more serious than they care to consider.
As you say, they keep finding ever more characteristics of the universe which completely alter what was previously thought, so it may well be there are processes going on that would account for those features currently ascribed to the singularity.
If I may, I would like to repeat the point which did raise my ire, in explaining a 12.6 billion year old galaxy cluster within BBT. What everyone seems to conveniently ignore is that all these galaxies did not, theoretically, coalesce out of the initial singularity, which theoretically would be quite dense and hot, but out of what existed after the inflation stage. This would have been far more diffuse, given that the inflation stage expanded the universe out the the point that the initial curvature is not measurable. Which is effectively to compare the visible universe to an area on the surface of this planet sufficiently small that the curvature of the planet is not measurable. If you consider this, it would mean that galaxies had to condense out of radiation probably about as dense as the intragalactic, interstellar medium. Ie, slightly more dense than the intergalactic medium. While this is obviously quite possible, it would require an incredible amount of time, so thinking it could have happened in one billion years is ludicrous, since it take almost a quarter of that amount of time for our galaxy to make one rotation. It is, as you say, a real physical anomaly.
Personally I don't have any trouble with the idea that space is infinite, because it solves the entropy/energy problem. Energy is never lost, because it simply radiates out to other areas and is gained by that radiated from other areas. This creates horizon lines, as we can only detect out to the distance radiation can travel before it becomes too diffuse to detect.