As I said - you cannot register your dependents here on Swiss insurance unless they actually live here - as the premium calculations are based on the assumption that you will make use 99% of the time of the Swiss healthcare system and its associated prices. Further, coverage is per capita and not lumped per family. Wild guess was rather tongue in cheek.

As to your other dilemma, you could continue under your US coverage and forego Swiss insurace to the extent that your US coverage is deemed at least equivalent to Swiss minimum legal insurance. This is determined by the authorities of your future residence canton.

In short, if you want a headstart, you can contact said authorities and ask them whether your current US plan qualifies as sufficient.

The only way to avoid this is coming here on a diplomatic posting.