Gene, Am in same boat as you. The only thing I could find that seems to fit the bill is through full tilt karting at the englishtown raceway. I am headed there Saturday to speak to them and go round in circles on their tag kart. They seem to run more than just arrive and drive services. I will ask about racing leagues etc. for us older farts (I am 47) and will let you know what they have to say.
Keep me updated on what they say. Also try to get them to tell you the popularity of the different available series/classes.