The position you are taking about is the lower oesophageal sphincter, this is aprox midway between your belly button and your sternum.
It could be the leaking of reflux after eating that is causing the pain. As it is only connected with your eating I would presume that it is a reflux problem.
Have you ever tried when you are experiencing this, pressing in on the painful area to see if it helps?
I also agree with James, you do need to get a manometry and a PH study done, this will show if you are having reflux and if you are a good candidate for surgery.
There are many people who have regular reflux and don't really feel it burn, and with others like myself just the slightest amount will burn, we are all different. It could also be that you are having some non acidic reflux which of course the ppi's will not help, this will also show if you get an impedance PH test.
Try some gaviscon advance after all meals and see if that eases things.
Hope you feel better soon,