The value of being able to make one book per day is linked to the price of a book, which means that on the island, the CPI and the stock market have to rise and fall together. That causes the stock market and currency to move inversely.
Because if you want an answer, you aren't making changes to the example that will help you understand. You're introducing confusing factors that are not needed. The original example gave a neat little illustration of how wealth-as-measured can drop without money disappearing. Don't bring CPI in to it (and stock prices don't drive the CPI so that is a reasonable assumption).
If you want to argue that the two move inversely then go ahead and don't mind me, but you might like to add in some evidence or case studies. And you'll need to be precise about real vs nominal, and probably start modelling other effects.
this is incorrect
CPI is a tool for adjusting the value of a dollar, but it doesn't have any bearing on the value of the total economy vs the value of all the dollars in existence. All the dollars in existence might buy the entire economy many times over or they might buy a tiny fraction of it. And that ratio changes continuously (both from money creation and economic activity). There is no inverse relationship mediated by the CPI.