Is it realistic to think there are agencies who are willing to work with me during the late afternoons/evenings and weekends while I am still working full time teaching until the end of May?

The problem is most people here are real estate investors, have no time to chase people around, or look for services to chase people around, so often is the case, if it's unpaid rent, put it in for collections, and let collection agencies handle it.

My agent was adamant about showing it to me, even though it was not on my vetted list of properties (probably because it was a dual agency situation?).

@Ricky Jefferson, If you manage your properties yourself, perhaps you could spend 10% of your gross monthly receipts on a part time bookkeeper familiar with the kind of (rental property) bookkeeping you need, from an employment agency such as Accountemps, etc.

My experience has been, these "First Time" or "Income Restricted" Loan offerings by various State and Local Agencies are all done through a Typical Lending Company (Mortgage Banker / Mortgage Lender) that has qualified with the Agency(s) offering the program.For Example, if you met the criteria for a "Texas Vet Loan", and were qualified for the program, all the processing and workup of the Loan package will be completed by Blank (Generic) Mortgage Company.

But they are also the agencies that limit us to 10 mortgages type of thing. 

Eric Newman Samuel Pawlitzki is correct... if you sell that land for say $60,000 to a buyer the title agency you use will settle your the liens on the property before the title can transfer as clean title.

If possible, getting a part-time job that would serve dual purposes of income & benefit to REI (Home Depot, Prop Mgt, handyman, etc.) might be a good play.

If not, paying commissions is not a problem, provided you do not perform brokerage activities (representing buyers or sellers in an Agency relationship of properties you do not own).

@Hadar Orkibi, one trick to boost your credit score (sometimes significantly) assuming you pay your cards off every month any way as you claim, is to pay them off right before they report to the credit agencies.