I always just book my main hotel for the "night/morning" I'm landing as Well and tell them I won't be arriving until around 3 am.
As long as they have 24 hr from desk they are always good with it . I'll check out Smooci in the taxi and by the time I've checked in, grabbed a few beers, had a shower and freshened up it almost time for my companion to arrive.
For me it's always been the most convenient and ultimately best value option