Okay, I'm going to turn convention on its head. Should you be pursuing a Masters if you plan on being a real estate professional? I would also question whether the additional income you will generate with your Masters will have a good return on investment. I know it isn't in Civil Engineering or Real Estate Investing. If it is a Masters of Business, I'd recommend you start a business and get your education through the school of (not so) hard knocks. If the answers are yes, I should be getting a Masters and yes it will provide a good return on my investment, then I would say you should let your future earning potential pay for you Masters while you take your current capital (cash and equity) and invest it in cash flowing properties. If you make reasonable investments (not, great, reasonable), you should be able to equal or beat your interest rates on your past student loans.
Because even if you just equal your 7-10.25% interest rates in cash-on-cash returns, you still have phantom gains in equity getting paid down and the possibility of appreciation.
If I were you, I would save the $20K as a rainy day fund and then take out 50% loan to value mortgages on the two properties you own and rent them out. Then look for two (or more) more properties that can cash flow a decent amount of money. Ideally you could find a multiplex (duplex or better) and house hack it as an owner-occupant.
In the end, the best part of acquiring another couple properties is it can "diversify" your portfolio so to speak. Even if you acquired the new properties in the same area (you could buy in another area to diversify locations), it allows you to diversify your risk into more units. If one property goes unrented, it's only 1/4 of your portfolio as opposed to 1/2. That's good business acumen if you ask me.
On the issue of poor credit score, I would recommend discussing your plans with a couple smaller, local banks and see what they say. If they knew you were willing to put 50% down on your new property, I bet they'd be much more apt to listen. There isn't a lot of risk for them to loan out 50% of the value. Even if things went sour, I'm sure the bank could see that they're isn't any risk of getting their money back. And in the end, banks are really just weighing their risk.
All of my suggestions are based on mitigating the risk of taking cash out of the existing properties by only taking out 50% of the value. You can certainly ramp things up by going to 90% loan to value (assuming the original poster (op) would qualify for the loans naturally) on a number of properties but it doesn't sound like the op is open to that at this time. Plus, I think leaving a margin of safety is a good thing and a 50% margin of safety seems very reasonable to start with.
And lastly, if the op can't get traditional financing, that's when they could get into private lending (hard money, etc.) to work out some creative financing with property owners like owner financing. You have some serious collateral (2 properties) to get some sort of loan. The terms may just be a little less than ideal (although it's doubtful that they'd be impossible to overcome).