The sound deadener material ("sdm") is a rubbery petroleum product. It is an incoherent mess of polymers. It could well have absorbed any of the several solvents named on the can's label. If so, the non-drying you're observing is in the sdm, not the paint solids themselves, and you could have a tough time returning it to its normal dry consistency because the 50 year old matrix of acceptable goo has absorbed similar-polarity solvents and isn't letting it go so fast. It is not simple evaporation. Ways to hasten this process: air exchange (run a fan over it) and heat, but not so hot it starts mis-shaping. Sunlight could be effective. Could take a lot of days.
You might steal an inconspicuous sample of the sdm, and take before/after closeup photo of applying a bit of the rustoleum.
Or tear that old crap out and install Dynamat. Much better in all ways.