Regarding psychotropic (and other restricted) medications

Hi.

I'm interested in looking into a prolonged stay in Japan, maybe temporary residency.

I take take Fluoxetine, Quetiapine and Methylphenidate. As far as my knowledge goes, only the first is outright prohibited. I'm close to the end of a two-week stay in Tokyo, for which I got a Yunyu-Kakuninsho, but it's to my understanding that that's only for up to a month's supply.

Is there a way to continue taking Fluoxetine, or if I wanted to pursue something like this would I have to switch to a legal alternative? Would I have to get a prescription from a Japanese doctor for the other medications, or would my Canadian one still be suitable?

Thanks!