I ultimately settled for ANA VISA Wide Gold Card. It starts with 1% cashback in ANA miles (assume 1 mile = 1 yen for now).
If you use ANA Pay, it rises to 1.1%. If you then convert the miles to ANA SKY COINS which are worth 1 yen each, having the gold card lets you do the exchange in a very favourable rate, up to 1.6x if you have the patience to save 50k+ miles before the conversion to SKY COINS. Conversion to SKY COINS also effectively extends the expiration of miles by one more year, but in practise the extension is lower than that due to slow accumulation of miles. https://www.ana.co.jp/en/jp/guide/amc/skycoin/skycoin/
So, stacking those multipliers we get: 1% x 1.1 x 1.6 = 1,76% which is great.
Worth noting that the card costs 15400円 per year, and a family card costs 4400円 per year. If you go for the family card, you can count everyone's mile balances together for one big SKY COIN lump sum conversion to meet the 50k+ most favourable exchange rate.