Laura Olson wrote:
 As soon as I was 5 hours
> away and stopped for a picnic lunch at a rest stop, the van would not
> start.

  Feeling somewhat cocky, we started home and it started
> happening again, not far from Billings, Montana.

Since you did not describe the behavior completely, I am assuming that
the starter does not make any noise or turn the engine, rather than
cranking without firing.
  I have had three vans that have had the same symptom, after driving
for two hours on a trip they would not restart. The solenoid would not
activate, apparently because of too much resistance in the circuit,
especially at high temperature.  The problem was solved in all these
vans, 76, 80, & 84, by adding a relay.  Eventually the starter on the 84
had to be rebuilt since the solenoid circuit ground connection is thru
the starter, when the brushes and commutator get bad they add a lot more
resistance to the circuit.
  I would certainly try adding a relay like the one that I believe is
sold by Bus Depot.

Good luck,
Larry A.