There is no way to avoid the war any longer. The invasion has happened.
You are oversimplifying to a dangerous degree.
There is at the moment no legitimate Ukrainian government. Putin is a vile authoritarian asshole, but he is right about one thing: Yanukovych's de facto removal from office was a coup.
Yanukovych can still make a claim of legitimate legal authority to invite Russian troops in.
And some part of the population in Crimea wants them there.
So, an "invasion"? Not clear.
As for "an existential fight in the west", it's doubtful that Putin wants to absorb all of Ukraine. Keep in mind that Ukraine is a synthetic state, based on the "Ukrainian Soviet Socialist Republic" set up by the USSR...which was created with a bunch of ethnic Russians exactly to keep Ukrainian nationalism in check. All in all, letting Crimea go back to Russia might be in everyone's best interest...but only if it's handled in a legitimate way. Right now, nothing happening over there has any legitimacy.