You can't boot Japenese original games with an American unmodded console, yes they're both NTSC, but they are different forms of NTSC (China, I'm not sure what form that is.). However you can burn the original Japanese game to DVD-R and then boot that in any region PS2 using an appropriate swap-trick with an Action Replay / Gameshark (new version don't work). The reason the backup will work and the original won't is because the backup has no protetion on it at all, and under the right swapping circumstances it will boot, however the original still has region protection and this is read and the game will not boot.
Your best solution if you do not want to get a modchip is to wait until Swap Magic 3.0 is released and get that with the DVD bootup disc and the DVD-RIP over 80min discs and make your own swap tool.
Here's a quick summary of some stuff you should know about the swap if you do have an old Action Replay / Gameshark.
1) The disc is about 71mins long and you cannot play dvd-rip games 100% correctly if they are bigger than this amount, the reason being, the PS2 laser won't seek beyond 71mins.
2) The Swap Magic 3.0 disc is supposed to overcome the above problem.
3) You cannot boot DVD backups using the swap-method without an original DVD game. If you want to boot a 2gb DVD backup you will need at least a 2gb original DVD game as well as the Action Replay / Gameshark.
4) Swap Magic has a DVD and a CD disc to boot DVD games (so you don't need an original) and the CD will not play games properly above 71mins, some will not even load up. Again Swap Magic 3.0 is meant to be the definite solution.
5) If you do a swap method you can get a flip case for your PS2 which makes it a bit like a Gamecube (the way you load games) although altogether this costs more than buying a modchip. Or you can take the front of the tray off your PS2, the thing with the Playstation logo and make a swap tool which can move the white cog where the tray is.
Important: New model PS2s referred to as V7 have double protection, you cannot play ALL games such as Tomb Raider and Splinter Cell using a swap method properly if you have a backup from an original version of these games (there are more too) without getting a protection removal patch, Swap Magic 3 is meant to get around this too. So as you have it, unless you have an Action Replay / Gameshark disc and PS2 which is around a year old or more, the chances of you playing a legit version of this game on an unmodded PS2 is slim.
Similarly, backing up your game is illegal, getting your ps2 chipped is illegal, ripping a game to cd or modifying in anyway is illegal etc.
All the information presented above is entirely legal in the form that it is and should be taken as guidence only, any mods if you feel something doesn't comply with forum rules etc please edit it as appropriate.