Using a Prism script, I can get Prism to import my data. But how do I get it to do an analysis?

There is no need to script the analysis. Prism analyses and graphs are always linked to the data, so if a script opens a Prism file and then imports data, the analyses are re-run automatically to update the results. The trick is to make sure the file you open already has the analyses in place (you can erase the data before saving).

Conclusion: Just script the importing of data and exporting of results. The middle step is handled automatically by Prism, so long as the Prism file has the linked analyses.