Cramming the tent into the frame bag isn’t much fun, and the result is not satisfying. The tent is not well compressed and it feels like there is lots of space in there that is basically wasted.
So I experimented with stuff bags that would compress the tent well enough to avoid any bulging of the frame bag, i.e. that have a diameter of approx. 10 cm, and re-claim some of the wasted space.
The final result are two small bags, one for the outer and one for the inner tent. They have lids and a compression strap, and fit well into the frame bag.