I would advise to avoid using HTMLService, it has a lot of issues with multiple user accounts and if you are planning to release it to the Marketplace you will start to see problems pretty soon.
As Martin mentions, the best way is to do the processing server side and let the user know by email once it's done. In my add-on I show a GIF as spinner plus change the color of the sheet tab to let them know that something is running and provide a REFRESH button to rebuild the UI getting the latest information.
Additionality you can use a spreadsheet to give immediate feedback, adding an image, change the value of a cell, etc.