Thank you everyone for such helpful advises. The links you've provided gave me a pretty good idea of what the prices are in Japan. On the good side touring bikes are not as rare as they're in Poland. I think we will try everything before we'll think about buying a used bike.

As for the airlines, talking to them is really flustrating. I've tried calling them both in Poland and Germany and also we've contacted them via e-mail. All the answers were pretty much negative. There's no more space for a bike on the plane. Talking to them really makes you feel like you're trash and they don't care about individual customers. Even though it clearly says at their site to contact them AFTER booking/paying for the ticket. I'd honestly recommend to avoid Lufthansa if you're traveling with a bike.

There's been a lot of very useful comments about how to pack a bike to make it look like a luggage.
We can check the bike as a luggage but it has to be no more then 158 cm all dimensions added. So I might be able to pack a bare frame to fit the requirements. It's not going to be easy since it's a Koga Miyata touring bike with over 100 cm wheelbase! Another luggage will be full with wheels, handlebars, seat and other components. Downside to this is what if they take bike one way and refuse to take it on the plane on the return? Also I was really hoping to get some unique bike stuff in Japan and now I probably won't since I won't have spare luggage space.

If this won't work we will probably try to find a used bike inTokyo or try to rent one. Buying in a recycling center isn't really possible if you're an outsider andThere's been too much funds and effort spent on this trip to let it go now.