In order for a home to be approved for FHA loan it must pass an appraisal. The appraisal need to verify that the heat is working, roof is free of leaks, electric is on, and hot water is on. There is few more things that I did not list here but these are the most important. It's really hard, and almost impossible to find a bank owned property that will meet all this conditions since the homes has been vacant for a long time until the bank finished the foreclosure action and were able to market the property.
As you mentioned, looking in other neighborhoods might be the solution since you can probably get a fully renovated one family in Jamaica in a price of a bank owned property in Cambria Heights.
I currently have the largest inventory of bank owned, short sales, and renovated properties in Queens in the following neighborhoods: South Ozone Park, Richmond Hill, Jamaica, Saint Albans, Hollis, Queens Village, Laurelton, Rosedale, and Springfield Gardens.
I think I might be able to help you find what you looking for in the right price that will fit your budget. Don't hesitate to give me a call on my cell @718-200-3140
Have a wonderful day!
Isaac Benshabat/Lic. Real Estate Broker