My JIS bottom row is currently:

<Meta> <Super> <Alt> <Control> <Space> <Control> <Alt> <Super> <Compose/Meta> <Greek>

I have left Control mapped to Meta, {,Mu}Henkan mapped to Control, Kana to right Alt, right Alt to Super, Menu to Compose/Meta (tap/hold) and right Control mapped to Greek.

I use keymapper[0] to do low-level remapping and tap/hold, and a custom XKB layout for the Greek modifier. I highly recommend this setup.

[0]: https://github.com/houmain/keymapper