Here is an excel spreadsheet that embodies Hoppy's formula to calculate the PAR (top portion) and the spacing between the LEDs (lower portion). I included Hoppy's suggestion to round off the PAR value. The spreadsheet is protected except for the input cells to prevent loss of the formulas, but you can unprotect it if you are so inclined (there is no password).
I notice that your spreadsheet also requests to use "half the optic cone" angle. Which is a reference to other posts where Hoppy and other have said that this is the area of most intensity.
You do use the same equations Hoppy used above though. IE, you're still dividing the cone angle by 4.
Is this how the equation in the original post of this thread is meant to be used? It makes sense to use the "effective angle" for PAR (half the optic angle, so 20 for a 40, and 40 for a 60), but making sure that Hoppy did not already account for this in his equation?