Just stayed at the Hotel Nikko Kansai Airport for one night after arriving from HKT via SIN at 21:30. The hotel is conneted to the airport on a walkway just passed the JR station; used the luggage cart all the way to the room. I really enjoyed the short overnight stay and the included breakfast was very good; large buffet with multiple islands for different cuisines. Rates were Y12500 room only and Y14000 with breakfast.

I do not know what their options are for day room use as they have a 2pm checkin policy, so perhaps you can contact the hotel to ask, otherwise it would likely be a 2 night charge to check in at 06:30 unless you vacate by 12:00 or maybe there is a late check out option at some extra charge?
https://www.nikkokix.com/en/

Update: Just found this info translated from the Japanese web page on accomodation questions:
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In case of early check-in (early check-in)
*Check-in from 6:00 a.m. to 9:00 a.m. 50% of the room charge
*Check-in from 9:00 a.m. to 2:00 p.m. 30% of the room charge

In case of extended check-out time (late check-out)
*Until 15:00 30% of the room charge
*Until 18:00 50% of the room charge
*After 18:00 1 night's stay

*Depending on the plan, the above regulations may not be met or your request may not be accepted.
*Depending on the date, we may not be able to accept your request.
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Cheers,

-Cyborg