If you were to use Power Query, you would need to recreate the connections, not sure if that is possible if you didn't develop it.

The general thrust of what I am saying is:
- build an Excel parameter table of all the variables that you want
- build queries for all of the datasources (complete data)
- in each query read in the relevant parameter(s) and filter the data
- load the queries into the datamodel.

Power Query helps because you can read the datasources as you can with PowerPivot, manipulate/transform that data, and then load into the datamodel. PowerPivot, or regular pivot tables, can then access that datamodel.