General, I think the US comparison is a bit over drawn. The US system has more fundamental differences than just having a President. In the US the Executive Government is deliberately separated from the legislature. Without the jargon, what that means is that all of our ministers are members of parliament, in the US the ministers are not allowed to be members of congress. It is a hard division between legislature and executive which a Westminster system, like ours, does not have.
We don't have to go down the US road, we can look for a better way to do this.
DS