Ok first things first how are you planning in tapping into that current equity?
The three ways you could do that is a refinance, a second mortgage, or a bridge loan.
The first two are only available BEFORE you were to list or even talk to someone about selling, as the lenders don't like to do "short term" loans. They make their money on people keeping the loans and paying the interest. The Bridge loan is made for this type of thing. The problem is that rates are normally high and their is the issue of how long it will take to sell your home. In the time you would be taking to sell your home you would have three payments:Bridge Loan, New Home Loan, Current Home Loan.
So when you go to buy the new home the mortgage company will take into account all those expenses when qualifying you.
The next part is the using the remaining equity after the sale of your home to lower your monthly payments. This is called recasting, and not a lot of mortgage companies will do it. Normally what you end up doing is putting the payment to the principal therby lowering the amoutn of time you will have till it is paid off but not your lowering your payment.
So basically you could do what you are talking about with a bridge loan and then getting a new loan that is recastable.
It doesnt matter that the sellers are doing For Sale By Owner. If you have any further questions you can contact me at firstname.lastname@example.org