To possibly answer you first question regarding cooling rate comparisons, I would refer you to "Transport Phenomena in Materials Processes" by Poirier and Geiger which describes in detail heat transfer conduction in solids of various geometries.
In comparing the cooling or heating rate between bodies of various geometries, Figure 9.6 on page 228 of the mentioned reference book provides the following temperature history;
... the time it takes a cylinder of R radius (or square rod of L semi thickness) to cool to within 1% of thermal equilibrium with its surrounding fluid is approximately 50% longer than for a sphere of R radius of the same material.
The cooling curves that could be used to predict temperature at the center of the body to establish a delta T/delta time are known as Gurney-Lurie charts. These can be found this book.
If you can determine the cooling rate of a round bar of radius "R" with a length L (to assume semi-infinite length), the cooling rate for a sphere for the same material and radius R will be 50% faster.
If you need more information, I would contact a reputable heat treater that may have actual data for cooling rates of round bars. I don't see how the sphere diameter will be of any use in terms of cooling rate and Jominy hardenability comparisons because heat conduction will occur from the center of the sphere out toward the lower temperature fluid in equal directions, so the radius makes more sense for comparison.
