You would know Japanese Law better than any of us, but in most other modern nations as long as you are legally an adult your parents cannot prevent you from leaving. They can of course call the police and claim you are a danger to yourself etc...but when the police interview you all you have to do is appear normal and aware and say you are in no danger and they have no basis to hold you. Unless a court gave some legal pyschiatric hold you are as free as any other adult to move around despite family meddling. The worst they can do is hassle you.
With regard to preemptive reporting you'd be a better judge of the culture there on that one. It would be seen as weird in some places, no big deal in others. If you were going to do so I'd tell them you were planning to travel but have overbearing parents who will likely report you missing and you wanted to make it clear you are an adult, of sound mind, and traveling of you own free will. Personally I'd skip it and deal with the police if I had to only.
I cannot remember if you live alone or not. You can use this either way. You can set up house checks for when you are gone with your local prescint/department/substation (law enforcement). It is something people do where I live when they want to make sure their house stays secure and no one breaks in while they are away. These things stay logged until the end date. It pretty much just increases patrols in the area. But it is a written record of absence.
With doing this it:
One, it lets the police know you will be gone without looking all weird.
Two, if there is a report put in on you for being missing it will subvert that by you already telling them when you will be gone. Put a fake day back so there is a timeline. You do not have to tell them where you will be going but just that you will be gone.
Usually in most 1st world countries a missing persons report generally only goes into effect 24 hours after the person is "missing" unless the person has a very strict schedule or does something so consistently that it is very odd that they missed it (i.e. calling mom every day at 2 pm). With only having one check you wouldn't be in the more immediate cocern unless you have been acting really weird these last two weeks.
What I would do is make plans. Tell your parents you are going out to eat, library, a movie, concert, walk around, something around the time you are to get on the plane so that you have some buffer time. With an event that lasts 1-2 hours you should be good. By the time they think you are missing you should be already on your way. No way for the police to track quickly where you went or even that you got on a plane (speaking from my countries stuff).
