IOW, as I read it, Morowitz is saying that after the universe experiences its heat death . . .,
I think you are reading it wrong which it isn't hard to do since it rather poorly written. The article you posted is basically a criticism of James Coppedge who cited Morowitz, -- a biophysicist and Robinson Professor in Biology and Natural Philosophy at George Mason University, with a Ph.d from Yale where he was an associate professor of biophysics, something not noted in the link.
Well, after re-reading it, I think my interpretation is correct. the 10340,000,000 odds figure that you quoted came from Morowitz's Energy Flow in Biology, and Morowitz's specialty seems to be the thermodynamics of living systems.
I wonder what "The Thermodynamics of Pizza" is all about! I also see an intriguing title: "Beginnings of Cellular Life, Metabolism Recapitulates Biogenesis". I assume this means that the metabolic pathways of current living things reflect the history of how abiogenesis happened. (You do realize of course that Morowitz is an evolutionist?)
A direct attack on Morowitz's assumption of a 239-minimum protein genome can be found in the critic of Coppedge at your link.
Yes, the discovery of self-replicating RNA (ribozymes) about 20 years ago is what got RNA-world theory started, as I understand it. That really reduces the required number of genes in a self-supporting cell.
IOW, as I read it, Morowitz is saying that after the universe experiences its heat death, it will be impossible for even one cell to form - spontaneously or not! - because there won't be any energy gradients left to tap into for the required energy.
After maximum entropy --"heat death" -- is reached, of course it will be impossible for a cell to form. It will be impossible for anything to form. The universe will be dead.
I don't think Morowitz or anybody would waste their time calculating the odds of anything forming at maximum entropy.
Your understanding is correct.
But there appears to be chemcial problems with the RNA World.
Something else to think about (from the link)
Furthermore, the relevance of ribozyme engineering to naturalistic theories of the origin of life is doubtful at best, primarily because of the necessity for intelligent intervention in the synthesis of the randomized RNA; then again in the selection of a few functional RNA molecules out of that mixture; then, finally, in the amplification of those few functional RNA molecules
A similar critque about the possibility of the RNA World can be found in the link in post 582.