The Golden Horde's biggest weakness is not religion but its weak structure, so changing its religion does not do much. The Golden Horde was elective but only to members of the Borjigin clan, which saw a lot of infighting for succession, you were lucky to even see someone rule the horde for ten years at times. This saw Mongol nobles look for aid, from Russian Princes regardless or religion, any talk of us vs them is exaggerated. the Borjigin clan where seen as Tsarivechi, or an imperial lineage in the same breath as the Roman Emperors and several Russian nobles did trace their lineage back to the Tartars. Not that I fully buy Eurasianism myself.
As for some kind alt-Rus formed by the Mongols, it's almost impossible. Stability issues aside, the full Kievan Rus, Novgorod included would see a massive demographic shift favor the Rus over the Mongols and the other tribes. City wise you have Old Sarai, possibly Bolgar, and maybe Astrakhan. Kiev still has potential even if it is in decline, You have Novgorod, Vladimir, Vladimir-Volynsky, Tver, and Smolensk. This is assuming the Khan really wants to actually rule the Kievan Rus instead of having them just pay tribute and go on the occasional raid.