The October 1976 PTE booklet for the Newcastle and Gateshead area contains both the route and timetable for the 638. As far as I can see, with the obvious exception of the Crawcrook/Clara Vale extension, it's the same route. I'm still trying to figure out what services were amalgamated to form this colossal route. The 138 is an obvious candidate, but, surprisingly, there are no Sunderland-Penshaw-Harraton-Washington services or Wrekenton-Low Fell-Saltwell services. There were services operating between Wrekenton, Washington and Sunderland, but these were probably forerunners to the 187/188->56 lineage. The 638 appears to be a truly unique creation.

On another note, I think I've worked out how the 639 came about.