I have used First Cabin once between long layover from international to domestic. Between 7 p.m. and 10 a.m. is overnight stay only. However, there is early mooning stay between 5 a.m. and 10 a.m. where you pay 3000 yen/3 hrs. After 10 a.m. you can stay at the rate of 1000 yen/hr.

Place was quite when I used the facility. TV in each cubical is by head phone only so you do not hear TV from neighbor. It is true you may not get a feeling of total seclusion in a room like typical hotel, but sliding blind fold instead of actual door does not bother you then I think it is fine. Cabin and shower facilities are segregated by gender, but shower facility is communal like gym shower.

You can make advance reservation via website.

Also, Hilton Tokyo does have day use rate, which is as much as overnight rate and only available from 12 noon to 6 p.m., I don’t see much of value. If the day use rate is as much as overnight then another idea is to book a hotel from an evening before your arrival and tell hotel you are checking in around 7 a.m. next morning.