I ended up booking LGA / LAX with UA and LAX / ICN with OZ, return with ICN / LAX on OZ and LAX / EWR on UA, all through ANA. The domestic lines had to be Y but it does seem to show in the UA app as a J class for the LAX / ICN R/T so I am hoping that UA will 1/ send the luggages to ICN and not make me recheck them at LAX and 2/ that they will accept the business class weight ideally.

I don't complain because I at least got to use those miles that were sitting at ANA and about to expire!