Your A-Line link is wrong.
Correct link
A''Line
The web site is in Japanese.
On Sunday 9th May, only A-Line is available.
Time table
NAHA 07:00→KAGOSHIMA 08:30 NEXT DAY
25.5h
Fare options and prices
Four options. From 35500yen to 14200yen
AIR
SNA is another airline of the route.The web site is in Japanese.
SNA
SNA may be not so different from ANA in price.Because SNA flights(2 per day) are code share with ANA.
But if you are lucky enough,you can use their VISIT JAPAN FARE service.
VISIT JAPAN fare | Skynet Asia Airways
I can't tell you can use the service on 9th May.