SkyVector.com shows 1282nm from PASY, Eareckson Air Station near the end of the Aleutians, to RJCN, Nakashibetsu, Japan, the closest airport I could find in northeast Japan.
No wind, 10 gallon/hr, that's 128 gallons of gas needed. More than twice what a 172XP carries? (50, 60 gallons?) So pretty much the equivalent of 2 passengers for the fuel and tank. Don't forget the cold weather overwater survival suit, not fun to sit in bundled up for 10+ hours.
Now, if the Air Force agreed to let you land there, and agreed to let you have AVGAS brought in, and if the winds cooperated, you might be able to make it with a big ferry tank installed.
You might have better luck departing from Adak near, Mount Moffatt, PADK. 1612nm.
The FAA site does not discuss fuel, you can check www.airnav.com for that.
Dutch Harbor, for example. Only Jet fuel is shown.
If you had the Diesel 172, that could make the trip a little easier logistically
If there is an eye popping spec for the JT-A, it’s the max range, 963 miles, an improvement of 323 nautical miles over the 640-nm range of the Lycoming powered Skyhawk.
That would help a lot!