I don't get this part of your formulation, Jim. In doing a profit rate time series, you don't want to adjust for changes in capacity utilization. The point is to measure the return on advanced capital over some particular set of fixed intervals. For Marx, the interval was a round of production; for us it's typically annual stats. Then you can look at things like capacity utilization rates as one of the many factors that the affect profit rate movements you derive. But it's only one of many effects.
More generally, the aspect of Marxian profit rates that is always left out of these discussions, though, is the effect of the turnover time of capital on the rate. Marx wrote a lot about it, but what he said is difficult to translate into today's world, using current statistics. Plus, when he left behind material for vol. 3 to be published by Engels, Chap. IV "The Effect of the Turnover on the Rate of Profit", (intended to be the final version on this topic, and in particular his full treatment of its effect on the rate of profit) there was nothing there but the title. Engels wrote Chap. IV himself. He had a lot to go on: the lengthy discussion of turnover time in vol.2, part II, covering chaps. VII to XVII (that's about 40% of vol. 2), Marx's Grundisse notebooks, which contains a passage (p.761) in which Marx puts turnover time in all its aspects right there with s/v and c/v as the main determinants of the profit rate. But unfortunately Engel's chapter leaves out much that is crucial. In particular, he never even mentions the effect of fixed capital turnover that Marx had emphasized. So it's left to us to flesh out chap.IV.
Turnover time is complicated, which is another reason (besides the incompleteness of chap. IV) it has been neglected (plus perhaps the fact that most people seem to mistakenly think it doesn't affect the profit rate much). There are five elements to it: time in production, time in circulation, asset life, the proportion of net fixed and circulating (roughly depreciation) components of advanvced capital, and the relationship between idle (e.g., inventories) and active circulating capital. For example, both the vintage (asset life) of fixed capital changes over time, as does the components of that capital (e.g., proportion of equipment to structures). It's important to capture these changing relationships because they directly affect the profit rate.
Obviously production and circulation time are knotty problems for stats. But the following can surely be done to reflect the other elements Marx was trying to capture. The Marxian profit rate should be calculated as surplus value divided by some measure of each of the elements of total advanced capital: net fixed capital stock at the beginning of a year, circulating constant capital for that year, average inventories, and variable capital (social subsistence of labor). Profit rate = s/K+c+i+v. That's the full version which can capture at least some of the main relationships Marx thought to be important.