Have you considered publishing tableau data extract of your excel file to tableau server. You can then add files to the published extract using the command line utility provided by tableau server. Developing the reports on that published data and then publishing that report to server might save you from re-publishing your report each time and also updating the extract. You'll just have to publish your report one time to the server (given that the report is developed on data from tableau server) and then each time you have files to add to your data source you can add it to the published data extract using the command:
tableau addfiletoextract --file "<filepath> --server "<serverpath>" --datasource <sourcename>" --username "<uname>" --password "<pass>"
also to refresh the extract you can use the command:
tabcmd login -s <server url> -u <uname> -p <password> refreshextracts --datasource <sourcename>
Also you can build your report directly using the data connection from SharePoint in tableau desktop, create its incremental data extract and then publish it to server. Then you can schedule the data extract to refresh automatically on a monthly basis from the tableau server. Then it will add all the data added to the SharePoint site in that month.
Thanks for your suggestions, Akash. I attempted to publish my extracts but encountered issues related to calculated fields: 'The data source you are publishing contains x calculations that reference a different data source in this workbook....'. I have many calculated fields across the multiple data sources, and different calculations for each workbook. I didn't figure out a way to resolve this, so I've gone with the following which is pretty clean so far:
-Save copies of each Excel workbook in our SharePoint library
-Map SharePoint library as a drive and edit data connections to use this path (mapping to the drive is key, as we previously attempted mapping to the SharePoint file paths directly which doesn't work)
-To refresh, edit charts and republish: Save latest copies of Excel workbooks to SharePoint library (Excel workbooks from ~5 difference sources); Select 'Refresh all extracts...'; Publish workbooks