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.
The illegitimate government of the United States I suppose should dissolve itself and place itself under its rightful leadership of the Queen, until such as time she and the British Parliament deign to grant independence?
What can we say about gross abuse of office (theft of $35 billion?) and the use of security forces as assassins of Yanukovich's opponents? How could Yanukovich have been removed "legitimately" under such conditions?
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.
Ah, but the letter of the law does not count with Crimea, eh? Where is Russia's right of armed intervention enshrined in law? If Crimea wants to join Russia the let it hold a referendum under conditions of peace, and without Russian coercion. Where is the logic that disorder from Yanukovych's misrule should award Russia with Crimea?