Man, this has gotten ugly...
OSU student here. Don't assume you'll end up on top, ever (duh).
If you're DC or bust, retake. GM isn't going to get you where you need to be, and as noted, there's been huge federal freezes. Way too much debt for not enough payoff.
It's not a cakewalk in Ohio, but there's a decent amount of profs who work in DC who are quite vocal about helping students, and as mentioned, the DC program. No, it's not your best shot at DC. I think around 5-10% of the class ends up in DC, and that's largely due to self-selection. Most people I've met want to stay in Ohio. If you're looking for work around Pittsburgh/WV, there's a decent amount of OCI stuff for those areas, and I've definitely met some Pitt/WV people who are intending to return. Again, nothing's easy now, but there are jobs with your background.
I would not do GM for what you're saying you want. I think OSU would give you a better shot at a job, and make it easier to pay off debt.