First, stop accumulating more debt.
Second, I agree with your wife — for one reason only. Yiu are likely to die first, and she gets an additional 8% in her base check for every year she delays. And she will get that, plus a COLA on that higher base check, for the rest of her life. Why rob her future?
Beware of those firms that tell you to stop paying and to set the money aside so that they can negotiate a lower rate. That can really ruin your credit.
BUT if you can earn enough now — extra money– to DOUBLE THE CURRENT MINIMUM PAYMENT ON EACH CARD — and keep paying that same amount every month (not the new minimum but the current amount) then you will have the card paid off in less than 3 years.
So instead of her taking SS early — how about you BOTH get side jobs now and make enough money to do that!! It’s a much better plan!!