Well Kazakhstan and Belarus can definitely be Russified fairly easily. I mean in 1991 Kazakhstan was already a few hundred thousand people away from being plurality Russian (they were 37%.) So with a bit more immigration, the area could easily be around 40% Russian, and all Slavs being maybe 65% of the population. Belarus has very strong connection to Russia already, and so with Russian education they could easily have the majority of their population speaking Russian and identifying as Russian IMO.
I think all the government would need to do is implement education from the ages of 5 to 16 across the entire Empire, and make it so that Russian was the only language of education. Obviously that's difficult to enforce, but it would happen in the majority of schools regardless. This will ensure that Russian becomes well known. Then have Russian becoming the only legal language of publication, from books to newspapers. Also, have radio and later TV from the 1920s to the 1950s only legally be allowed to be in Russian.
These measures wouldn't go on forever, but if they ended in 1990, by 2020 we'd still see Russian being widely spoken, and it would probably be enough for many Ukrainians and Estonians to see themselves a part of a larger Russian state. Combined with the upper classes, who likely would have been educated in Russia, descended from Russians or support the economic benefits of remaining Russian, I think you'd have a majority of people willing to remain Russian.
Alternatively, there are much more extreme measures that would work to an extent.
One option is have land reform actually take place in 1905 to allow for much greater industrialisation. This will allow for the Russian government to be richer to peruse these policies. If they want to be aggressive, one option is to fund the movement of hundreds of thousands of peasants from the Ukraine, Central Asia and the Baltics into industrial cities such as St Petersburg, Moscow and a dozen more. Then fund the movement of hundreds of thousands of Russians into these rural areas. In a place like Estonia, which had just 1,000,000 in 1900, the slow movement of people between 1900 and 1930 would be enough to make the county 20% Russian by 1930. I'd imagine this would happen in the Baltics, Kazakhstan and certain parts of Ukraine. Also, have resources be put in place for these new arrivals in Petrograd and Moscow, to give them access to some kind of housing and workforce. You can even include name changes for these arrivals in a dark mirror of Long Island.
This would likely form enormous diasporas of Russian minorities in the major industrial centres. However in those cities there will generally be more 'russification' as successive generations will learn Russia. Meanwhile in the countryside Russian birthrates will be higher, and so in the long game Russians will proportionally become much more of the empire's population. I'd also imagine in Central Asia, the natural resources will attract thousands of Russians, to work on the oil fields and gold mines. Combined with potentially hundreds of thousands of people moving from Central Asia to the industrial centres of Russia, we'd probably see enormous minorities of Russians and other ethnicities in these areas. Combine that with universal education in Russian and you've got your aim.