"WRT the prorogation, how would an elected HoS, with a supposedly non political role, have dealt with it?"
The phrase "non political" doesn't mean that the role would be purely ceremonial. A better description would be" Politically neutral", similar to a Supreme Court Judge or the role of Speaker.
Because an elected head of state's neutrality is prescribed by law, they can be genuinely independent of government, acting as an impartial referee of the political system and an extra check on the power of government.
If there's a risk that a new law may breach fundamental rights or principles, for example the proroguing of parliament, a HoS may refer it to the Supreme Court. Or if there is widespread public opposition to a bill, as with the brexit bill, the HoS could refer it back to the people for a second, confirming mandate.
The system we have atm means that governments can break laws, overide the fundamental rights of citizens with impunity , push through laws and sign treaties without the support or even reference to parliament and our present HoS is powerless to stop it.