I just had a thought...
Depending on the complexity of the report on the number of groups you have, you might be able to put the group header in a separate details section at the top of the details. You would then put a suppess formula on that section:
{group field} = previous({group field})
This way the "header" will only appear at the beginning of each group like it should and, since it's in the details line, should also appear in the excel export.
I haven't tested this, though, so I'm not absolutely certain it will work.
-Dell