Here's an answer- I hope someone finds this useful.
After a few changes including building MapPoints more similarly to the sample and I wound up seeing:
Submitted.
Executing...
ERROR 000816: The tool is not valid.
Failed.
in the JobInfo.Messages that were seen at the geoprocessor JobInfo.JobStatus upate to esriJobStatus.esriJobFailed
Next, looking at the ((ESRI.ArcGIS.Client.Tasks.ServiceException)(taskFailedEventArgs.Error)).Details, I saw:
"Cannot load the data file Dataset_conus for the geographic transformation NAD_1927_To_NAD_1983_NADCON."
After seeing that, I modified my Runtime deployment to include:
Client Core
Local Server
Geocoding
Geoprocessing
Spatial Analyst
Network Analyst
Map Server Results
Additional Projection Engine Transformations
So, the answer is: one of the above deployment options were needed.
[And, thanks for the suggestion, Kuiper.]