It sounds like a great idea!
However, rather than extending the actual PlantUML server with rest API, we'd prefer to create another server than would only serve REST. This should fit your need.
Now, we have absolutly no idea of what kind of REST service would be easily used with Spotfire, and we have no experience at all in Spotfire.
If you have some Java knowledge, the easiest way (for us) would be that you start a project somewhere (on github for example) with a mock REST service that you will be able to use with Spotfire.
For example, this REST webservice will take a text diagram in input, print it on the standard output, and generate a dummy/hardcoded PNG image.
Once you will have initialized this, it will be easy for us to add the missing part (that is, the real diagram generation using PlantUML.jar library)
What do you thing about this ?