The First lounge doesn't have individual sleeping rooms either, just a separate area with a couple of lounge chairs. It's facing towards the common area of the terminal and has open ceilings, so it's pretty noisy. The First lounge doesn't open until ~7am (business: 5:30am).

The thing about the airport hotel is that, AFAIK, you can only rent rooms for "day use" starting at 8:00-20:00 or as an overnight from 20:00-08:00. And it's not exactly cheap either. Someone please correct me if there are other options available that I am not aware of.

Have done this transit a many a times, arriving 5am and flying out at 10am. It's not something I look forward to. My routine has been to slowly walk over to the business lounge and once it opens, have a cup of coffee and take a shower right away. Showers at the First lounge are similar anyway (and nothing like the CX Cabanas ), so best take advantage of being first in line. Then over to the F lounge once it opens for some breakfast (which is not served until something like 8am IIRC) and a nap on the aforementioned deck chairs if needed.