Something Napoleon did often and made him slightly unpopular: force his satellites to provide a certain number of troops. As it stands now, your satellites have to much freedom in this and it takes ages (even when sending war subsidies) for them to build up a decent army. So I would suggest this option (coming at a big relations penalty) to force them to take loans to build an army worthy enough of Mordor/France.
Vive l'Empereur!
Vive l'Empereur!