I am trying to purchase a second SFH investment property.

Hi Dave, Its great that your taking a pro-active approach to be prepared to purchase over the next few months. 

Hello everybody, I am looking to purchase a property with a section 8 tenant, and the rent is way below market at about $800 for a 3 bed house, while an average rental is about $1300 to $1400.

@Sarah Sullivan - We had an investor client purchase a 3 bed 1 bath brick ranch on a crawl space with fairly accessible plumbing fixtures.

For example: Using $500,000 as the purchase price, the difference in your DP is $50,000.

One year is a blip for an RE purchase.  

Is it feasible to obtain a loan or a good old boy agreement where a lender offers 100% financing for both the purchase price and construction costs at hard money rates, secured by a second position on the borrower's other properties?

With an FHA loan, you are not going to be bringing hardly any capital to closing (compared to a conventional 4-fam purchase with 25% down).   

You could do delayed purchase financing, this would allow you to refi without the seasoning but you would only be able to pull out 80% of what you paid + 80% of your completed rehab.

We did purchase a SFH to live in as we have grown our family so we would no longer be house hacking.