The cohesion value we use to describe soil strength is not an inherent property of the soil, but rather an artifact of the assumption that a curved strength envelope can be represented as a straight line. The cohesion is literally the y-intercept of that "idealized" linear strength envelope. The tangent of the friction angle is slope of that straight line.
The approach that the geotechnical consultant took appears to be standard practice for many parts of the U.S. For loading conditions that are slow (with respect to the time that it would take for excess porewater pressures to drain from the embankment), we will use a "drained" type of analysis with a higher friction angle and lower cohesion (most often selecting zero cohesion). This case is the embankment without the train. For loading conditions that are so rapid that any excess pore pressures that would be present in the soils would not have a chance to drain, we will perform an undrained analysis and generally select strength parameters, cohesion and friction angle, from a strength test that is run rapidly without the ability of pore pressures to dissipate. this is the case of the embankment with the train.
The reason why the results you have may seem to be contradictory may be that the clays in the embankment are unsaturated (have high suction values) and that choosing zero cohesion may be significantly underpredicting the actual strength for the longterm case. One approach to handling the effect of suction is to select a cohesion that reflects the effect of the suction. There are various ways to do this.
If you would like to have a more realistic estimate of the stability of the slope over the longterm, I would suggest that you get in contact with the geotechnical consultant that wrote the report and ask him/her to assess the potential that the clays in the embankment may be unsaturated and have suction values.
If the consultant is unable to make such an assessment, there are various suction experts that would be able to assist you.
On another note, the embankment has been in place for about 100 years and it hasn't shown signs of instability yet your report tells you that in the long run it is supposed to be less stable. This should tell you that one or more parts of the puzzle are not yet in place.
The results of any slope stability analysis should reflect the actual conditions and performance of the embankment.
BBC&M Engineering, Inc.