Back in June, I asked and Airport hotel said they only offered the reduced rates for daytime stays (gone by 6pm?). OP is going to be arriving at midnight, so will have to pay full overnight rate even if checking out after 4hrs.
I had the same response when I was inquiring a few months ago for a trip in November; quite disappointing, as I had taken advantage of the 4-8 hour booking option before and it was very welcome, but they know seem to have restricted this to local daytime layovers only.