Pectoralis
When introducing user research to an internal organization you should be precise at how you will output your research to the team, so that it can be fully understood and throughlythoroughly discussed.
In my experience when handling complex research there are a few ways to approach the stakeholders and to organize all the findings later on.
As you mentioned contextual inquiry with individual stakeholders is a way to learn more about the problem space, as you are dealing with multiple potentially different use cases perhaps a survey will be a good starting point to identify pain points more generally.
If you're adopting a 1:1 interview with the stakeholders, be sure to adopt some sort of insight downloading after each interview to organize your insights (Matt Cooper from Ideo has some good articles on the subjetctsubject - here).
As you are working with a desktop application, perhaps an usability test will be a good approach to both talk to the stakeholders and discover usability issues within the application itself. You can use the research sprint from GV applying also the five act interview.
To organize your findings you'll need to find behavioral patterns in your user base, because just because people are from different departments that does not necessarily means they behave differently around a desktop application.
In order to do that instead of using personas I've come to adopt the Jobs-to-be-done approach, since it approaches users in the specific tasks they want to complete whilst also providing context and motivation from the task. You could still create a empathy map to aggregate both demographic and psychographic findings into a easy visualization.
Furthermost presenting those findings to your stakeholders will also require some effort, the best way I've come to find is to create stories that stakeholders can relate to, that approach is heavily used in Airbnb and Uber alike as it is a powerful tool to get your point across.
I hope it helps with your research.
Cheers,