Here are few tips that I would suggest.
If you do not need live data from Vertica, please consider using extract. Extracts are often faster than live connection.
You can calculate your measures i.e. calculated fields in Vertica and then Tableau will use them as pre-calculated fields.
You can make use of sheet swapping techniques using action filters to show/hide some of the sheets. I would show two departments first, but if your boss wants more, than he/she can show other sheet using action filters/parameters. You can check this example.
Finally, you can design guided analytics. Let your boss first choose year, then month workbook will show. Once he/she clicks on month then Tableau will show worksheets with filtered data.
I just have one concern, why you are using parameters rather than simply using filters.
Thank you for your input.
1. We can't use TDE's as it is against our policies. We have to use a live connection.
2. If you'll look inside of the workbook, you'll see that the calculations that take place are close to impossible to put into a table in a database. I am open to solutions, though.
3. Swapping sheets is out of question as everything has to be on a dashboard at the same time.
4. Bosses don't care about guided analytics. They just want to see the report.
5. With filters, after you save the workbook, the report date defaults to an older date, which is a big waste of time. However, using parameters, we are able to default to the most current date. See workbook.
Thanks again for looking into this.