ArtVivant usually organises yearly exhibitions of Amano artwork where you can actually purchase limited print runs. I've attended a couple of times in years gone by but am unaware if they have been held recently - still have a couple of free posters and clear folders from attending.
Seems like you're going to Tokyo at the wrong time OP, as you've just missed this;
http://amano-exhibition.jp/
EDIT: Blogpost from a random salaryman who attended the event, detailing how he chose and purchased a painting [JP]
https://takayuki-art.com/picture-of-yoshitaka-amano/
EDIT 2: Failing to track something down in person, try calling Art Vivant with a translator if you cannot speak Japanese or check out places like
Mercari or Yahoo! Auctions JP.
EDIT 3: $10K comes in at around 100man at the moment so that should definitely be more than enough to get something - either by yourself or through a translator helping to ask around if you are willing to pay. Best bet is to contact Art Vivant if you want an original otherwise you may have to be happy with just a numbered print - good luck OP!
EDIT 4: Scrolling to the bottom of here;
http://artvivant-fantasyart.net/ finds that they are touring Japan in the next month or so! If you could get someone from JapanERA to help out or pop over on a plane, you could 100% pick something up at the Tokyo event in Aqua Plaza (where I attended the aforementioned previous events)