I think we can rule out any ambition on Slaine's part to rule over people. Everything he does is for Asseylum's sake. It would be wholly uncharacteristic for him to have any such desire to become the new emperor or take over either the Vers Empire or Earth. He doesn't seem to particularly enjoy violence either, so we can assume he doesn't want the war to go any longer than it needs to, i.e. if there is a way to end it, to put a stop it all, then he'll do it.
If he wants the war to end as soon as possible, why is Lemrina not making speeches demanding that the fighting cease?
I know this is all leading to an asspull where the true nature of Aldnoah is revealed to us and the power to destroy a moon is suddenly either Slaine or Inaho's, but Slaine doesn't know that.
I won't say it's Valvrave levels of ridiculously stupid bullshit yet, but it's Code Geass R2 levels of stupid. The protagonist-wars in these threads are fun (#teamSlaine vs #teamInaho), something R2 didn't have since no one liked Suzaku.
I 100% watch for the protagonist wars in this thread and elsewhere.