Thanks for all the useful feedback. Results on some follow-up on my own...
My local JD dealer indicated the most efficient implement would be the three-point hitch Frontier 1048 4 ft core aerator. It has an operating weight of 316 lbs (prior to adding any additional weight) which should work fine with my 2305. And does a great job. However, as JDFANATIC pointed out pricey at around $2000. Unless I can find a second-hand model, the JD Tow-Behind 48-in plug aerator could be an option. However, it is primarily for the X500 and X700 series garden tractor and a little small (according to my dealer) for the 2305. Although would enjoy adding the Frontier aerator to my implement collection, must also question the investment for perhaps 2x/year usage. I will also follow-up the Trac-Vac 3pt suggested by kvjohndeere.