Verilog-AMS variable with randomly selected value at each Monte Carlo sample

Dear community

I would like to create a Verilog-AMS module where a variable is initialized to a random value for each sample in a Monte Carlo analysis, i.e. something like that:

integer seed;
real random_value;
analog initial begin
    seed = $random;
    random_value = $rdist_normal(seed, 0, 1.0);
end

Problem: random_value never changes in a Monte Carlo simulation. Why? My understanding is that $random returns a new number with every call - at least that's what the documentation claims. A look into the log files confirms that the seed indeed never changes,

Additional note: I am aware that Spectre actually does not exit with every MC iteration. ADE assigns a certain number of point to a job. But even setting the maximum number of points per job to 1 in the monte Carlo form does not change the outcome.

Another note: It is technically not the best practice to achieve the randomness by just setting a random seed, and then drawing one sample from a probability distribution. Rather, the seed should stay the same during the whole MC analysis but every iteration draws another sample from the probability distribution function. Is there a way to achieve that?

Thanks in advance for any help.