I'm not sure I follow your interpretation of embedded taxes in regard to what Boortz and Linder discuss in their book.
Embedded taxes refer to those taxes which are spent for components or products bought by the retailer (for instance, if I'm a baker, when I buy sugar for my cookies, I have to pay a sales tax on that sugar, plus the sugar's embedded taxes from the sugar refinery, which must buy the sugar from the cane producers, who must buy it from the cane farmers, who must buy land for their farms... etc etc.) All of those individual taxes add up and divide out, so that a little bit of the cost of paying all those taxes ends up in the sugar that I buy for my famous sugar cookies. Under the FairTax, however, embedded taxes (all those taxes added up from buying the sugar from the distributor who buys it from the refinery which buys it from the farmers which rents the land from the landowners) would be removed, thus lowering the cost by, ON AVERAGE, 22%. That number would obviously change depending on the goods in question, because not all goods go through the same amount of production, and not all goods are taxed the same. The basic idea is that, regardless of actual reduction, prices would go down by, on average, the same amount as the FairTax itself, meaning that all produced goods would AVERAGE OUT at about the same amount, on top of the elimination of federal income taxes, SS taxes and Medicaid.
Unless I've totally missed your point.
First as a business you don't pay any sales tax on the sugar so there is no money to be saved there. The sugar refinery has maybe 22% embedded tax costs but they are mainly the income taxes and FICA taxes paid to their employees. This money is going to be paid to the employee not retained by the business as a cost savings according to the FairTax proponents. So, at most the sugar refinery drops his price by 10%(by keeping the employer portion of FICA and a few percent compliance costs). The cane producer is in a similar boat, as is the cane farmer.
So if you look at the whole chain- the cane farmer save 10% of his costs so he drops his price 10% to the cane producer who is able to save 10% of his costs (which includes the ten percent he saved on the stuff he bought from the cane farmer) so he drops his price 10% to the sugar refinery aho is able to save 10% percent of his costs (which includes the ten percent he saved on the stuff he bought from the cane producer) and so he is able to sell his sugar to the baker for 10% percent less.