Thank you for the helpful pointers. I ended up writing an R script to produce a textfile in the correct format for import (using the GENERATE command) as a 'route' coverage in ArcGIS.
The route format retains the directed nature of the edges, and edge i->j and j->i can be displayed simulataneously using a cartographic line offset.
The format is
route-id
measure[order],x,y
measure[order],x,y
END
e.g.,
1
0,850,7945.694
1,850,6906.463
END
2
0,850,7945.694
1,2650,6386.848
END