You'll receive a Level I certificate no matter what Level I class you take. All avy schools do that.
Exum Guides are in rarified air. You are talking about the best of the best with that group. There are just a few outfits that can stand with them. So yeah, you can't go wrong with Exum. I would highly recommend learning from them.
Don't know much about the ast lvl 1 course but I just did some quick reading and it seems like its recognized by the CAC (Canadian Avalanche Centend. to that end I'm not sure its associated with aiare? Then again you said this will be in japan so perhaps there's a bit more recognition to it.
The AST course is basically the Canadian version of AIARE from what I understand. Canada is also at the forefront with avalanche science and most US programs are basing their curriculum from Canadian ones. So yeah, it's a quality course to go with AST.
I can't speak to the backcountry course but I did the Steep n Deep camp a few years ago and looking back now, believe I got a bargain for it. I'm sure whichever guide you choose will be money well spent.