What options are there for security on shared data sources for SSRS?
We are in the exact same scenario.

What you could do here is to deploy the projects into different environments / targets on the report server. For example you could create different "folders" in the reportserver and deploy it multiple times. Then configure the sql login with different passwords there once and prevent to overwrite the datasources during deployment to protect it from getting overwritten. This can be configured in the project's settings.