We bank with one of the biggies, and keep separate US and CH accounts. Given the complexities of being an American abroad, this is the solution that works out best for us.
To make it simpler, choose US and CH advisers who are used to working together.
Oh, and once you have experienced the wailing and gnashing of teeth that is part and parcel of life under FBAR/FATCA - do drop your senators and congressional representatives a note describing the difficulties you encounter as you do your bit to promote US interests abroad...