There is no built-in mechanism to turn of all but one constraint in a class, unlike the in-line random variable control that would effectively turn rand_mode off for all but one random variable.
You could set up an array of bits to use in an implication constraint
control[0] -> {block_of_constraints};
control[1] -> {block_of_constraints};
...
And then it would be relatively straightforward to set the control bits any way you want.
Having 100s of unique constraints in a class seems a bit unusual, you may need to explain further what you are trying to accomplish.