This may backfire though, since people could simply turn on the Western companies and say "hey Putin was right, they ARE out to get us". Stoking protests again

This may backfire though, since people could simply turn on the Western companies and say "hey Putin was right, they ARE out to get us". Stoking protests against the Russian government using the very same tools you mentioned above sounds like a more promising route. Maybe there are still factions inside Russia's political apparatus that are powerful enough to decapitate this government. Not that they will hear "the will of the people", but they may sense an opportunity to take Putin down and enrich themselves, while cutting down on the USSR imperialism nostalgia.