Realize the Russians are not trying to win this war. They want to pressure the Ukraine government to stay away from the EU/NATO (...) As soon as the Ukraine gov gives up the war will disappear.
That is to win the war, just not by military means. You make it sound like Kiev could stop, then Russia could stop, then things would be fine. Ukraine is the second poorest country in Europe, only beaten by tiny Moldova. They need good trade relations either with EU to the west or Russia to the east. Traditionally it's been east. They were in talks with the EU to open up to the west. The president was trying to halt those talks and instead make a new deal with Putin, which lead to the revolution and a pro-western government.
The only way they could "stay away from the EU/NATO" would be to basically give up on everything they've stood for and that people have died for and come begging on their knees to Putin for a new trade deal. Quite likely they'd have to formally surrender Crimea and rebel controlled territory in the east to Russia too. That's close to unimaginable and it'd probably start a new war of secession in western Ukraine. So the talks with the EU/NATO must continue while the conflict areas will be used to interrupt and delay the process.
At this point it's only a question of how long they can be kept in limbo. But the EU has shown before with Cyprus that they can accept nations with territory they consider illegally occupied, without taking any action. Whether they'd have the balls to do it with Ukraine is a different story, but it's not an absolute blocker. Already things are opening up with the association agreement, it looks like visa-free tourism is going to happen... they're heading down that track whether Putin wants them to or not.