Everything I have read here is good advice, yet surf is infinitely variable so I guess you're plan must suit the day.
I often beach in light surf at the same spot and find that it's when the boat gets Sideways in the Driveways that things start to unravel.
So, for normal light shore-break before entering the foamy break-zone, I first lean over the side and with a practised move insert the Cart.
The cart wheels contact the sand first like a soft anchor while the boat is still floating so if the boat is struck from behind by more broken waves it always aligns with the Swell and keeps the Bow pointing at the beach.
This gives me extra time and stability to hop out and scamper around to the Bow to grab the handle and pull the AI clear.
A giggle-bonus is when onlookers see you pulling an AI out of the water which then magically keeps running up the sand on unexpected wheels, I'm sure many think I sail that way
