I wonder if he ever thought about what he'd do after finding and killing Schmidt/Shaw.

I don't wonder this at all. I feel sure that he has clear plans that go far beyond Schmidt. I think we see an inkling of that in his Geneva hotel room where we see his map of Europe, but most of my feeling on this issue are from the scene with Erik and Charles the night before they go to Cuba, the one where in my interpretation Erik is saying subtextually something like "Charles, I know you read my mind back there at the CIA facility and you know my plans. You knew it was never about peace for me. You know that once I kill Schmidt I move on to the next part of the plan and this temporary alliance of convenience I formed because you and Moira could help me kill Shaw will be severed. But I like you and would want to keep working with you if you're willing. Are you in or are you out?"

But again, I saw the movie I wanted to see, not the real movie. I have no barometer to tell me how legitimate a reading of the film this is.