but once there I discovered a hotel right in the middle of the two terminals--there's a connecting bridge, so you can walk there directly.
As well as full-night rates, they offer hourly rates between 9am and 6pm.
BEWARE: Once you clear customs and enter the terminal lobby you will be agressively greeted by a
few men at a counter selling hotels--avoid them and go look for the above mentioned hotel by yourself.
Unfortunately this is what happened to me--I didn't discover the better option till the next day.