"ignoring the fallacious idea that the first proteins were made from amino acids combining all on their lonesome."
Oh, so there had to have been something else present for life to form....good point....the genetic machinery that tells the cell how to produce protein...the DNA. The problem is that both both DNA and protein depend on each other for existence, and you are assuming that "The genetic machinery that tells the cell how to produce protein and the protein required to build that genetic machinery both originated gradually" So not only do proteins need to be generated by the clever and smart (don't say intelligence that is a bad word) chance machine, DNA needs to be generated at the same time by the same clever and smart chance machine at the same time.
Even if polypeptides had formed in the primordial soup, hydrolysis would have broken them up and destroyed most amino acids. Organic compounds such as amino acids, tend to break down when dissolved in water. The higher the temperature, the faster this breakdown occurs. …joining many amino acids together to form a protein with a useful biological activity is a much more difficult problem than forming amino acids in the first place. The major problem in hooking amino acids together is that, chemically, it involves the removal of a molecule of water for each amino acid joined to the growing protein chain. Conversely, the presence of water strongly inhibits amino acids from forming proteins…..
This and other problems w/ spontaneous generation posted here:
http://www.freerepublic.com/focus/f-news/1689062/posts?page=185#185
There could be a interesting section or two added on the probability of designed enzymes as part of a discussion of some of the types of reactions you mentioned (enzymes are often required).... typical bacterium, which is the simplest of cells, is made up of 2000 enzymes...And of course, the formation of enzymes is but one improbable step in the formation of life....I will try to add that if I can find time.....
You're a bit behind the times, current thought is that RNA was the first self-templating molecule, and that it originally catalyzed protein synthesis while DNA later took over its role. A gorgeous book on this topic is
Singularities by Christian de Duve. It's not so much targeted towards laymen as some popular science books, but you'd probably get a lot out of it still.