Can I salvage cookie dough made with whole eggs instead of yolks?
If nothing else, the egg whites have added additional liquid to your dough, so maybe you can compensate by adding more flour.

Try taking a small portion of your "batter" and add a little flour to it. See if that brings it closer to the consistency you expected. If you can determine how much flour is needed to fix just a small amount of the mix, then you can apply it to the whole thing.

If it doesn't work, you'll still have your Plan-B to fall back on.