Starting with Vesey's list (https://boxd.it/1otZK), I added three movies from DapperGaffer's list (https://boxd.it/mooTm):
Carmen Comes Home (1951)
On Wings of Love (1957)
The Stormy Man (1966)

To that list, I added five films from this BFI List "Where to begin with Japanese musicals" (https://www.bfi.org.uk/features/where-begin-japanese-musicals):
* Hometown (1930)
Tipsy Life (1933)
Singing Lovebirds (1939)
Carmen Comes Home (1951)
** Tokyo Cinderella (1954)
The Stormy Man (1957)
* King Drummer (1967)
* Hong Kong Rhapsody (1968)
On Wings of Love (1957)
* Young Guy in Hawaii (1963)
The Happiness of the Katakuris (2001)
Tokyo Tribe (2014)
Memories of Matsuko (2006)
Princess Raccoon (2005)
* Pink Lady The Motion Picture (1978)

The titles with one asterisk beside them are new to the list. The title with a double asterisk does not seem to be on Letterboxd.