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Simple.The pope has to consecrate Russia to immaculate heart of Mary with all the bishops.

I expect a pendulum effect thanks to the rise of the internet. When young people today are genuinely curious about Catholicism, they don't head to their DRE or RCIA first, but rather begin online. Now, there's every mixture of error here as well, but that's where God's grace comes in to steer well-meaning individuals in the right direction. Not so long ago, real Catholicism wasn't potentially at your fingertips like it is now.

I also think the time of large-scale deliberate infiltration of the Church is largely in the past for a few different reasons. This allows the mainstream Church to shift more organically.

Right now, you'd have to still be very liberal to be willing to seek ordination from the mainstream N.O. Church which is the most likely path for future Church leadership, but I still think a very slow shift of the N.O. back toward God will ultimately be the resolution. Each individual will decide in their own place and time when it's safe to return from their respective lifeboats and I don't expect to be one of them.

I'd presume a very pessimistic timeline on this due to my assumption that if the Church were to steer somewhat in the right direction, it would awaken her enemies and once again be a major target.

History repeats itself. 

God provides the remedy when mankind humbles himself and acknowledges that he needs His help.

When the Western Schism took place men tried to fix the problem and made it worse.  Councils were held to elect new popes.  At one point there were 3 claimants to the chair of Saint Peter.

The remedy to the Western schism was an act of humility and an act of complete trust in God. 

The True Pope at the time called a council to elect a new pope and then resigned so that this could be a valid option.  The 9 day wait period of "sede-vacante" took place and then a new pope was elected. 

(See: Von Pastor's "Lives of the Popes" as a source for this.)

As for what might happen in our times...

I could not say for sure.  That is in God's Hands.  

That being said...  I think that unless a person who most recognize as pope is the one to initiate the Restoration of the Church or resign and elect another better in his place who would accept it?