Currently, you have a savings rate of 47%: (4400-2108-768 + 12500/12) / (4400 + 12500/12). This is a great start, and already puts you on track for financial independence in under 18 years, even with your negative net worth. A couple of small adjustments could bump you to a 60%+ savings rate and FI in 10-13 years.
First, realize that even though your situation is great, you are playing long ball. Paying off student loans and achieving FI takes on the order of a decade, unless there are rare circumstances. For a single earner, it happens $3-5k per month, one month at a time. It's hard to accept this with a NW that is a year or more away from even hitting 0, especially in this community where there are so many monster success stories (our NW is now -$45k, down from about -$130k, so I fucking know). So, while you are optimizing your finances, you also need to set about arranging your life in a way that makes you happy.
Here's my opinion:
1) Spend a few months putting together an emergency fund. In my opinion, the E fund is mainly there if you lose your job. It's all well and good to use your credit card as an E fund when you have shitloads of stock you can sell to pay off the CC/heloc/401k debt, but to me it looks like if you lost your job tomorrow you'd be kinda fucked. Your bare bones expenses are currently about $2k, so I'd save up $6k cash for a start, maybe scaling back my discretionary expenses for a few months to get this done quickly. It will be a drag to delay paying extra on your loans for another few months, but you're trading a little extra SL interest for a huge increase in short-term flexibility. You might be surprised by how this little cushion affects your financial stress. If you really want to be frisky with the credit-is-my-emergency-fund-and-my-job-is-stable thing, you could invest this money instead of letting it sit in cash.
2) Yeah, probably move eventually. I would take this nice and slow, because your current situation is not precarious, and you mentioned you just got out of a long relationship. Take some time for yourself; avoid sudden changes for now. When you're ready, have a casual conversation with your LL. Maybe he'll let you out of your lease right away. Maybe he'll list the place on Craigslist and let you out when it rents. Maybe he'll let you out for a fixed buyout. Maybe he'll be a dick and hold you to the remainder of lease (the law always gives him this option, though he must make good faith efforts to rent the place if you vacate). I've broken an absurd number of leases in my 7 years of renting, and all of these are possible. It doesn't hurt to ask, and breaking the lease can't affect your background/clearance in any way (short of just randomly terminating payments and getting evicted).
Switching campuses near where you want to live does sound good, but you'll have to investigate all the details--is it really plausible to get transferred there? How will your rent change there? Exactly how much will it knock off your current travel budget? How will it affect your career long term? When you do move, you can optimize commuting by minimizing C(x) = 10x + 4(D-x), where x is your distance to work, and D is the distance between work and F&F town. Guess which value of x makes C smallest :)
While you're taking your time on your time to think about (2), think about expanding your social life where you live. There are lots of things you can do, but one great way to meet people as an adult, with lots of collateral benefits, is to join a CrossFit gym. The cost may tighten some Mustachian sphincters, but it is healthy, fun and highly social. Of course there are lots of other avenues.
In general, I think you should be able to save $500/month on rent/hometown trips in this category, maybe more, at some point between now and one year from now. This will kick your savings rate into the 60% ballpark.
3) I'd be VERY against buying a house in your situation. Why shackle yourself to a permanent residence when it sounds like you haven't figured out much about your career and living situation yet? See here:
http://jlcollinsnh.com/2013/05/29/why-your-house-is-a-terrible-investment/ Also, homes and taxes in your state are notoriously high.
4) When you've saved up your emergency fund, I'd consider cranking your retirement contribution to the max. Yes, this will slow your SL repayment, but it will save you a lot of taxes and get you more tax-free growth. Remember, long ball.
See you at 0!