In that situation my wing is usual pierced by the foil so I roll it up and paddle in

4 major repairs last summer.
In small waves up to head high I hold the wing up above the wave and take the wave on the head, board at the end of the leash as far away as possible. Between sets try and get out of impact zone as soon as possible paddling on the board with the wing trailing or get up with the wing if you can. Wind can be sketchy inside the break. I have caught waves lying down in smaller surf to clear the impact zone.
In bigger waves we have started chucking the wing, prearrange this with others so someone chases it down for you.