If you are going to turn around and sell it, it would not pay if you have any closing costs. For example, let's say you lower your payment by $200 a month but paid $2000 to get the loan. Then sold the home in one month, You would have just lost $1800. If you get a no closing cost loan you do not have that problem, but the lender would lose the $1800 because they paid those closing costs hoping to get a higher rate.
That is why the fact that you have had the property on the market will be a problem, but many lenders will do it if you take it off the market and sign a letter saying you intend to stay in the property. See if the lender is still paying those closing costs in return for a higher rate if you do a no closing cost loan.