You are correct. The sweep recordings cannot currently be controlled via SCPI. This has been requested before and is something we hope to add to our software in a future release.
Until we can add this to the software, there might be another solution. You could use the API and store the data in the SHR file format. Located in the SDK, you can find an example SHR file parser project. From this project, you can learn about the file format and use the API to retrieve sweeps to store in your own SHR files.