To a minor degree I accept your argument, primarily because the Moscow Patriarchate has called itself “The Third Rome” or, more boldly, “The New Rome”.
It was the Grand Dukes of Muscowy who coined that term after the fall of Constantinople.
Moscow considered and to a large extent considers itself to be concurrently
1. A regatherer of the Mongol khaganate. First competing with the remnants of the Golden Horde in Kazan and Astrakhan, then conquering the Chagatai khanates and into Mongolia proper
2. A gatherer of the Orthodox after 1453.
3. The ruler of pan Slavicism
These 3 have driven state policy since Napoleonic times
But more properly, I object to calling them Byzantine as it was a western European way of “othering” the Roman’s in Constantinople and forgetting that from 450 to 1200 the most powerful military and economic state in Europe was the Roman empire based in constantinople.