The information you provide would lead one to guess that there are 3 sorts.
You are correct in saying that early (SI and II) hinges did not allow the bonnet to open fully. As you say that SV hinges interfere with the grill, you could deduce that SIII hinges must be different to both SII and SIV/V because SIII bonnets open wide and yet the SIII still has the SII grill.
However, the Parts List only lists 2 sorts, and as the later one supercedes the early design, it should be interchangeable. I know of a SII with later hinges that all works fine so it could be worth looking very closely to see why yours doesn't fit properly.