To avoid (fuel/carrier) surcharge, you can redeem with none/low surcharge carrier such as QR/JL.
On or after 01 June, IMHO, redemption on JAL will be no FUEL surcharge.
See JAL's FUEL surcharge table in
Originating in Japan
https://www.jal.co.jp/en/inter/fare/fuel/table.html
Originating outside Japan
https://www.jal.co.jp/en/inter/fare/..._overseas.html