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I would think if there is that much flex in your tyres there is not enough ply in the walls, and probably the tread as well. Stepping up the ply would fix it, I think.
I have run Nankang light truck tyres on my boat trailer and box trailer for about 8 years, with no issues. I regularly put 2-3 tonnes into the tandem box trailer, and it only has 165x13 tyres. Never had a problem.