Parliament

Another way is like in the Netherlands where members of cabinet cannot also be members of parliament. If you want to join the executive, you must vacate your seat in parliament. So you can't wear both hats at the same time. The cabinet can also include people that didn't appear on any ballot. Thus you get a strict separation between the executive and the legislature. Not even our prime minister has a vote in passing legislation (which also why legislation gets passed just fine even if it takes a few hundred days to form government, the executive is an optimisation, not a requirement).

Indirectly elected representatives (that is, people elected by elected representatives) are no less legitimate that directly elected ones, as long as the first layer of election is reasonably representative (i.e. any form of MMR).

The requirement to speak as one voice is because the cabinet consists of multiple parties hashing out a common position. If you don't like the common position, you're free to leave, or more likely, convince your party in the legislature to vote against it.

(This system was born out of the last set of culture wars, we'll see how it holds up this time.)

All of this is pretty far from the OSI board though.