For Eurasian Empire feelings you'd probably want Alexander III. It's somewhat more plausible. Most of Russian elite considered themselves Europeans (there were of course
slavophiles too, but they were not a mainstream).
Anyway, you'll need a very compelling reasons to move the capital like when Bolsheviks moved to Moscow after Petrograd become a border city (and too associated with the former establishment). Or you'll need a Tsar with iron hand and iron will like Peter I to move the capital because he likes it. The move would affect millions of people and most of them would be unhappy especially if the move is arbitrary. Nicky would not have the guts.
But it is possible for a slavophile Tsar to move his own residence to a city deeper in Russia or even build a new one without provoking too much of an outrage. With the deveopment of modern communications it may eventually become a new capital if he lives long enough or his successors like the place too.
Moving to Siberia is trickier, and before aviation it is too far to be realistic. Incidentally, I've read somewhere that Denis Diderot advised Catherine II that Ekaterinburg would be more logical place forthe Russian capital for the same reasons as OP

I doubt that Catherine II ever considered it even if such talk happened in reality.
In more recent times moving to Siberia would be possible. It could be done to give boost to the region, make it more then resourse provider. There still would be needed a very determined state policy and a lot of money to pull it through.