What we really need for the Russian Empire to transform itself internally is a major attitude change within the predominately culturally and linguistically Russian, Orthodox political establishment/aristocracy: the ability to see that the smaller nationalities can and will be loyal to the Tsar and the "idea of the Empire" even if they speak their own languages, follow their own laws and customs and practice different religions.
IOTL, in the 19th century the smaller nationalities were seen as suspect, very much capable of betraying the Empire at the drop of a hat if they were allowed any trappings of Nationalism. The Polish, of course, were the poster boys for nationalist trouble, but clearly even loyalty did not stop the threat of Russification. The Grand Duchy of Finland was as loyal to the Tsar as any ordinary Russian province, and by the end of the century the Finns were losing the constitutional rights (they thought the Tsar had promised to safeguard) so fast their heads were spinning.
The main competitors of Russia, France and Britain, were already culturally and linguistically unitary states, and very clearly strong for it.
The foreign examples were very tempting. So, how can we avoid the OTL situation, in which Russification was seen among the political elite as the vehicle for unifying the patchwork of suspect nationalities into a strong, God-fearing Empire under the divinely ordained power of the Tsar? How to make the Russian aristocracy and royalty of 1830 vintage multiculturalists in a few generations, at the same time avoiding the strengthening of Russian (imperial) national chauvinism AND the smaller nationalisms of the minority peoples?
Having more liberal, reforming Tsars is all well and good, but getting to the rank and file of the aristocracy, the intelligentsia and the Church is more than a miscarriage or a nihilist bomb away.