The Eav des Bavx ASB is the way to go. However, in the summer I prefer a traditional AS to a balm or milk. I usually go with Speick ASL. I find that its scent is dissipates quickly and avoids clashing with the Eav des Bavx edt.
Eav des bavx is one of my faves, so I too hve been trying to find a good as match. So far I think alt innsbruck is the victor. Nice tobacco-y scent that fades pretty quickly and doesn't clash