I'm glad to read that you have modified the wheels already, I didnt want to be the smart arse to post that that wont work.
I have found in testing such skinny wheels that they will drift sideways each time the sail gains power/speed, giving you a scalloped shape track down the beach. Youve got quite a good sail area there so I am putting money on exactly that happening if the wheels dont collapse.
A set of 8" rims and 4ply ribbed tyres would be an improvement I think.
However, please do the experiment and post results, GOOD or BAD, as this will help others down the track.
Welcome to the wonderful,tricky world of designing and buiding landyachts

there are some really satisfying moments ahead