This is a more acceptable way of saying it, but the problem I have with that view is this: you just said "God TRIES to save everyone" Obviously, not everyone is saved. So...This means that there are some parts of His creation that God has no control over. That is not a god I want to serve.
We are DEAD in our sin, so even the power to accept or DESIRE to accept God comes from Him. Yes, God gives the offer of salvation to everyone, but dead men can do nothing for themselves. Say we as humans were in the middle of the ocean, unable to save ourselves. If we were drowning or merely DYING, we could reach for the life ring that God throws to us. Since we are DEAD, we are incapable of doing even that. God must first make us alive, so we can reach out and grasp the life ring. WE chose to grasp the ring, but WE would never have even seen it if GOD had not opened our eyes and shown it to us. We would have remained dead in our trespasses, not even seeing or desiring the life ring.