To my knowledge they don't exist. The M4 was derived from the M1014 which was designed to comply with the gas operated requirement of the USMC shotgun contest. That gas operated design utilized Benelli's ARGO which, in a different form, was also used in their short lived auto loading rifles. If memory serves, were around the time of HK imports.
Welcome to the site. As far as the M4, I am fairly sure you'll have to settle for a much younger brother to your M1. However, in spite of some of us like myself being partial to the Benelli Inertia action, the M4's do fit into the collection nicely. If you are looking for a rare HK variant for your collection, consider an M3, it's a semi-auto/pump combo gun. They re-released it recently too though the original has a rare folding stock version that I am partial to. If you decide you want a rare M4, the NP3 model 11711 is likely the rarest of that model.
M3T Folders: