>In exchange for that, I would have to give up 3 other citizenships. Not a great deal...
Obligatory IANAL, but the "no dual citizenship" thing is a Japanese thing and it's not like the Japanese government will go around informing other countries of your new citizenship status. You would have to make the rounds yourself informing the governments concerned you renounced their respective citizenship.
Which is to say: I'm an American, if I went and got Japanese citizenship then the Japanese government won't care to inform the US government about the proceedings, nor will the US government care even if I personally tell them because the US government permits dual citizenship. Japan would care about my holding dual American citizenship, but again: They wouldn't care to inform their American counterparts.