I haven’t had the chance to look at your page yet, but my first impression is that the links are not recording the port information that were specified when the link was drawn by LinkingTool.
If you save the model, does your link data have port identifiers? If not, check how you initialize your GraphLinksModel – have you set its linkFromPortIdProperty and linkToPortIdProperty to the names of the properties that hold the port identifiers on your link data?
I fixed it by forcing these statements, right after diagram creation:
myDiagram = new go.Diagram("myDiagram"); // must name or refer to the DIV HTML element
myDiagram.model.linkFromPortIdProperty = "fromPort"; // force port link to/from property
myDiagram.model.linkToPortIdProperty = "toPort";