I've been self-employed for only 6 months, and loans are proving difficult to come by despite my great credit (not to brag, I'm moreso frustrated and seeking help).

In response to your original question, closing agents should handle private loans just like a bank loan. 

You can spread your cash out pretty far here when taking advantage of leverage opportunities like 100% purchase/100% rehab hard money loans.

If you are moving from your SFR to another property, then you should be able to get a 5% down loan or even 3% if it's FHA.  25% is only if you won't be living in the property in my experience.

(Auctions and foreclosures can also provide great leads.)With $20K, hard money loans are a practical option, as they emphasize a property’s ARV over your financial history.

I currently work with investors who are looking to begin their portfolio in turn-key real estate and manage for them on the back end so they can still enjoy their everyday lives while having a resident in place paying down their loans. 

The property is located near two colleges, so I’m focusing on student tenants and planning for 12-month lease terms.Do you have any tips or advice for renting by the room?

The only way to pay down a loan, is to pay down a loan.

Most mortgage companies will not call loan due if payments are current but you do run that risk and need to be prepared to payoff or refi at a moments notice.

Cash out should be used as a 12-24 month loan so that you can buy another property and pull cash out at the next 12th or 24th month mark.At that point you take a portion to pay off or down the first loan and use the rest as a down payment on the next REI.