Your central point here is, I think, absolutely right — but I would be careful about using the terms “neoliberal” and “neoconservative” in this framework. Neoliberalism is a specific set of policies and values that has to do almost entirely with economic and financial issues; likewise, neoconservatism is almost entirely a foreign policy and “defense” stance. These two sets of ideas are not mutually exclusive and do not sit on different spots of a spectrum (though their unfortunate names do lend very readily to such an interpretation). Neoliberalism has nothing to do with liberal social ideas one way or another — and neither does neoconservatism have anything to do with conservative stances on those issues.
However, I want to stress that this semantic concern does no violence to your argument vis-a-vis Clinton — you’re spot-on here.