(I realize that gacmd.exe and its Linux equivalent support this via a "-variables" parameter. I'd rather not install gacmd.exe on 70 servers to connect them to this project, which is why I want to use the web service.)
Really, it shouldn't matter (GET parameters are the same regardless of client), unless you're gonna tell me another API I can use in Java AND Progress without installing GACMD.EXE on 70+ Progress servers. <=)
This is resolved by RunProject Programmers Guide.doc, which says:
In addition to the above parameters, this service accepts any variables that were defined in the project. When posting the project variable, each variable name must be prefixed with "p_". For example, if you have a variable named "file" defined in your project and if you want to override its value for a particular execution, you would post a parameter named "p_file" with the desired value.