In my opinion, get a short term hard money bridge/construction loan. It's expensive, but you can close in 2-3 weeks, finish the job and refinance.
Lenders, Coney Island Capital Group, or Approved Funding Mortgage Bankers may consider it.
Ask for Jacob
Find out about a 203K loan, it is exactly what you are looking for. You can google that for more info and Lowe's is sponsoring a program designed specifically for owner/occupants and may be able to steer you in the right direction to get the loan for you. Good Luck.
Call Frank Tamayo of Metlife Home Loans-Appel, Evans Tamayo & Bach Mortgage Consultants@ 212-413-4548. I've been doing business with him for 10 years & he's the best there is. He also has a Park Slope office.