Hi Tim - Any time you want to potentially group by people, I recommend an assignment report. It creates different items for every assignee on a task or issue so that you can group them by Assigned To and it appears for each of them separately. I have a lot of teams that love it as it can combine tasks and issues as well as shows how the planned hours are split for a user.
The one issue you will run into is the team grouping. Are the teams that are interested in reporting like this the Home Team of your users? For my example below in Europe, the department is the Home Team so I can do this for Medical Writing and Creative. However, if a specific client wanted it, I could not as client teams are "other teams" for a user. (And for clients I tend to role based reports as we don't need the client all up in our resourcing of individuals.)