I don't think you need a densitometer for the Kodak test—the results should be fairly visible across the pre-exposed areas.
Originally Posted by cliveh
The issue with the coin test is that it does not subject the paper to a pre-exposure under the enlarger. The only exposure the paper gets is the safelight exposure. This way, you are testing the safelight exposure on a sheet of paper that has not crossed the boundary of its inertia. A positive outcome of a coin test is always a positive indication that safelight is not safe, but it will often produce a false negative, in my experience, with safelights that are only slightly unsafe, for example with old safelight filters, some LEDs, and so on. They will not fog the paper, but they will depress contrast just as a pre-exposure of the paper would do, which could be the reason OP is not getting the desired contrast.