So I hit this again for a stay last week at the Hilton Istanbul Kozyatagi, so I simply booked 2 separate stays online for subsequent nights.
At check-in they said they couldn't link them, but would handle it the next day.
Next morning at just after 7am I get woken up by the TV turning on and blaring noise at me at a far too loud level for any time of day, let alone 7am (just like it had been when I first got to the room the day before). I'm guessing someone at the front desk had handled the second booking and re-checked me in - in the process automatically turning on the TV to welcome me to my room...
From what I can make out, the stay (1 of them, as expected) and points did post correctly, but it looks like I've only been allocated 1 night rather than the 2.