Sumner says that I confused the "prices" and the "weights" and then referred me to the discussion of his initial post on the matter. William Barnett contributed comments, well worth reading. (Barnett also commented on my earlier post.)
Lars Christensen posted on the matter, tying the Divisia approach to Steve Horwitz's "A Subjectivist Approach to the Demand for Money." Reading about Divisia also brought that paper to my mind. Horwitz credits William Hutt's 1956 paper, "The Yield from Money Held."
Anyway, the difference between the benchmark interest rate and the rates of return of various financial instruments that provide monetary services are the prices of the monetary services. I was very much mistaken in treating those prices as if they are used as weights for the quantities of the different sorts of monetary assets too add them up to an aggregate.
According to Barnett, the weights always add up to one, and it is the prices (the value of the monetary services) that are being weighted. The weights are based on expenditure shares, which would be price times quantity. Barnett describes these as being "growth rate" weights, which I understand as being weights used to multiply the growth rates of each type of monetary instrument, and then summed to get the growth rate of the Divisia aggregate.
I realize that most macroeconomists focus on growth rates, I the past five years has shown how mistaken that focus can be. It was the large drop in the growth path of the Divisia levels that care clearly related to the significant drop in the growth path of nominal GDP, real GDP, and employment. Anyway, I am looking forward to more detailed study of Barnett's work.
Also, I should note that Josh Hendrickson, a young Market Monetarist whose blog is "The Everyday Economist," has been interested in the Divisia approach for some time.