I'd do the later arrival but I second the recommendation to get a day room near the airport (make sure you don't have to check out at noon!) or book your hotel for the night before and make it clear to them that you're arriving early the next morning. I've done the bleary-eyed walk till I could check in (and usually in the rain!) but I'm 70 and don't want to deal with that anymore.

I did run into a snag in India once- my flight from LHR arrived around 10 PM. I reserved the room the night before and noted in my reservation that I was arriving at 10 PM. Got there and my room "wasn't ready". I knew exactly what happened. Many international flights from India also leave at night. They'd collected money from me (well, my employer) for that day and collected money from the previous occupant of the room for a much-later checkout knowing I wouldn't show up till after 10 PM. They said the room would be ready in an hour and offered me a free dinner. I'd just had dinner on the plane. They sent me to the lounge. They were so gracious that I couldn't have a meltdown (not my style anyway) so I politely told them that if my room wasn't ready in an hour I'd be back. Fortunately, it was.

Yes, arrivals lounges are wonderful if you have access. A shower and a change of clothes can do wonders. Many have nap areas.