I've now completed this journey, so I'll add my experience:
I had no problems going through security/immigration at Haneda at 21:00 on the evening before my flight. I had printed out my boarding pass after checking in online - a self-printed boarding pass was accepted at each step. After immigration, it was a short walk to the transit hotel. I checked in there and after dropping off my bag went for a walk around the airside part of the airport to get a bite to eat. The airside part of the international terminal is open 24 hours at Haneda with a small gap in flights departing between 03:30 - 06:00 on the day I was there. From what I've read online, the other terminals at Haneda do close for the night (only the international terminal is open 24 hours).
The following morning I walked to the gate ~20mins before the flight - I had to step to one side at the gate to allow my passport to be scanned and my boarding pass to be re-issued, but this seemed normal for Asiana for anyone with a self-printed boarding pass (I saw another passenger going through the same procedure while I was there).
I was very happy with the whole experience - it was much less rushed than if I'd slept landside and much cheaper too! A double room for 12 hours in the "transit" part of the hotel (airside) was 15000yen (~135USD) while a double room in the landside part of the same hotel was 30000yen (~270USD). 135USD is not bad for a hotel in Tokyo and this was a nice hotel.
I emailed both the airport and the transit hotel before my flight. Neither of them were certain that things would work out for me and suggested I double check with my airline. I phoned Asiana's desk at Haneda and they said everything "should" be ok, but encouraged me to stay landside instead of airside "to avoid any problems". They were friendly, so I tried to find out what kind of problems they thought might occur and they said "immigration" (they might not let me through). They also suggested I should visit the check-in to get my passport checked for my destination (which I couldn't do in the evening before the flight as the Asiana desks would be closed). I pointed out that with a self-printed boarding pass I'd go straight through security without visiting check-in so it didn't matter - but they didn't agree on that! In the end they insisted I should stay landside, but I told them I couldn't easily change my reservations so I'd ignore their advice.
In the end I couldn't see anything that would have caused me a problem, but if I had luggage to check-in or couldn't check-in online due to some issue then I wouldn't have been able to do what I did...