How to have group column headers of different size in ag-grid?

I have a complex ag-grid table with several layers of group column headers. The ag-grid documentation shows how to set the height of group column headers with the groupHeaderHeight property. However, that sets the height of all group headers, not just a single row of group headers. When I set the groupHeaderHeight property to height of the tallest content, I get a table like this one:

Tall column group headers result in all group headers being tall.

We use a function to find the tallest header height and set the groupHeaderHeight to that value. As you can see, there is barely any room for the actual data because all group column header heights are driven by the tallest one.

How can I set up group headers of different heights so we can show more of the data in the table?