You might to meet the people in the neighborhood. Consider walking up and down a few streets on a Saturday late morning or early afternoon. If someone is out raking leaves or doing some work on their home, it is a great time to engage in a little light conversation. You can spot the "talkers" easily. They will not just answer a quick question, they will walk up to you to talk. In our business, we call these people "bird dogs". They tend to know a lot about the neighborhood.
After you explain that you are interested in the neighborhood, they will often volunteer who might be moving. If they don't volunteer any information, you might ask: "Do you know anyone around her who might be thinking about or planning to move?
It's the personal approach. I have found it to work
Do all that you can to get them to mention a figure first. Then be fair and maybe give a little to make it a win win. You can have an attorney write up contracts or if both you and the seller walk back iinto one of the real estate offices I bet you'd get more interest