@Voyager,
I think your original point--the Guide overstated the effect of quantity of one on payment--is well-founded. I also think that what you described about making and paying for partial deliveries when the quantity is one is ok.
However, I think you have one thing wrong. I think you concluded that progress payments under FAR 52.232-5 and -10 are payments for accepted services because they are excluded from the definition of contract financing payment at FAR 32.001. You may have even concluded that they are delivery payments. If so, I think you are misinterpreting the definition of contract financing payment.
Progress payments based on percentage or stage of completion are a form of contract financing. However, for purposes of the Prompt Payment Act, progress payments under FAR 52.232-5 and -10 are specifically excluded from the definition of contract financing payment so they will bear an interest penalty if paid late. This does not mean they are payments for accepted services. If that were true, there would be no reason to specifically exclude them from the definition of contract financing payment (or specifically include them in the definition of invoice payment).