If there was a whole bunch of PODs I could actually imagine 'Crimean Russia'.
(In OTL even Ivan the Terrible once run away like a rabbit from Moscow burned by Crimean tartars.)
The main POD should be a military and political genius in Crimea. Something like Mongolian Genghis Khan or better Manchu
Nurhaci (1559-1626).
If Nurhaci managed to
start conquering China having united 'wild' Manchu people we could easily imagine some Crimean tartar guy doing something like that with Russia on the other side of Eurasian continent.
Of course first of all this 'Crimean Nurhaci' would have to unite most of tartar Khanates which would mean recreation of Golden Horde.
And quite naturally this 'Crimean Napoleon' would not be a Turkey's puppet.
He might be wise enough not to defy the authority of the Istanbul (at least openly).
And the Turkey's sultan might be realistic and try to use this new situation to his benefit - having a new and powerful ally in the North would give him an opportunity to strengthen Turkish empire on other fronts.
And all in all I would give this new 'Great Crimean Golden Turkish Horde'

from 30 to 100 years. Why not?
Imo Russia got rid of tartar yoke not because Russia had become stronger. It was because Golden Horde became weaker (fell apart).