I expect the marginal PR gain from one of those charities being GiveWell-recommended would be pretty small.

Depends how much EA people are going to talk about it. I also think the whole is a good story for a journalist to tell.

The actual leverage of creating such a credit card would of course depend on uptake, and for an individual effective altruist, it would likely be better to find a credit card with a good cashback rate and donate the cashback, rather than using a charity credit card with a probably mediocre or bad rate.

If one of the EA organisations would go to Visa, I don't see any reason why they shouldn't be able to negotiate at least as much money as a good cashback card. From the perspective of Visa, giving money to charity is tax deductable. That might make it possible to get more money than the best cashback card.