You could rent out the home you're in now and move into the new home to get that low down-payment loan, assuming you have occupied your primary for long enough.

I plan on low balling an offer.

Unless you are highly leveraged and don't have much "skin in the game" as they say, your cash on cash return will be very low.  

If you're hurting to sell maybe go ahead and take the hit but if its Low DOM then maybe put it back out there and get some conventional offers that are willing to meet in the middle or make up the difference.

A lot of lenders may tell you the appraisal is free however its not free if you dont close you will still pay for the appraisal typically (its only free and credited back at the end or at the closing table).The other part is to make sure rates are where you want them to be (low enough).  

Hi Connor, This is my understanding on this type of loan.The FHA Loan  is mainly an insurance program by the FHA (government entity) that allows low down payment on the purchase.

I heard some contractors are building houses for low income owner for only $8000 flat  fees, but I heard the quality is not good I wonder how common dealing with that flat fees, I think it sounds fair, also as @Wayne Brooks I can add an incentive if he came under budget. 

Dues in my property's neighborhood increased by 20% right after I purchased because of a low reserve fund.

I would think if loans are secured by RE with low LTV, then you should get something back?

Interest rates are very low, take advantage of them.