Hi Keith:
Excellent question, thank you for asking!
The Runtime SDKs are used for building client apps that do not run behind web or application servers. As a matter of fact, (sadly, hopefully someday this will change) using the Runtime APIs in a Server (multi-user) environment is a violation of the Runtime license agreement.
It sounds like the recommendation for your use case would be to build and deploy a Server Object Extension (SOE) built with ArcObjects and deployed to ArcGIS for Server.
I hope this is helpful!