Alright, with a bit of research and sleep...
IS-4 did become IS-4M, but it was a small improvement involving side skirts, transmission tweaks, etc....
Major points in the development of the IS-4:
1. Kotin, a rival chief designer, hated the Obiekt 701. Rivalries in Soviet tank design had some good points and bad points, but in this case the IS-4 was always dogged by Kotin messing with it.
2. In 1950 the IS-4 was rushed to the Far East Military District to counter UN forces in Korea (there was worry of a UN invasion in the Soviet Union or Manchuria). With first hand experience of Soviet equipment (albeit in the hands of the North Koreans and Chinese Volunteers) there was worry about Soviet tank design and the aging D-25T gun was considered to be replaced by several other guns in development. Rearming the IS-4 was considered to be cost ineffective and unnecessary considering the development of the T-54, and the development of what would become the T-10 tank.
3. Deteriorating relations with the Chinese lead to the transfer of 80 IS-4M tanks to the Transbaikal region in 1967. Once again there were thoughts to rearm the IS-4M, this time with the M-62T2 gun currently in use on the T-10M. It was considered unnecessary especially with the combat debut of the BM-21.
4. All remaining IS-2M, IS-3M, IS-4M, and T-10M tanks were officially removed from service in 1997 by order.
I hope that helps clear it up a bit. Yes, no IS-4 tank had the M-62 gun installed. It would be a "fantasy tank" in that regard, BUT it was considered and feasible. Take it for what it is worth.