Shaun, select all those broken segments on the surface edge and enter the command "Merge"
It will turn them into a solid curve that is still integral to the surface edge.
You cannot Merge around "T" lines that intersect the edge.
But to make things faster, you can grab ALL of the segments and Merge at once will combine each total selection of broken curves within their own respective surface together, separated of course by the "T" intersections.
To cut them back up ANYWHERE, use Trim and "Add Trim Points"