I won't bother renting hotel, the only accessible hotel is Nikko and they are expensive. I would just stay at the airport til morning, and take the early train to main town. I had the same experience twice, and decided to stay overnight at the airport.

Or if you managed to beat the custom before 12am, you could take the airport night bus to Namba and rent any nearest hotel there. The last bus depart at 12:15am.

try airbnb... lots of houses nearby there.. i oso arrived around ur time and the house owner come and pick us up (with cost of coz)

but that is because i came with family got baby and toddler.. so it is not right to stay around in the airport that long..