boost::multiprecision random number with fixed seed and variable precision

I am trying to explore the effect of precision in one of my applications but its proving quite difficult. For instance it doesn't seem possible to fix the number of digits of precision at runtime.

Additionally, when using a fixed seed inside a rng, results are not reproducible when precision is varied. Namely, if one changes the template argument cpp_dec_float<xxx> and runs the following code, different outputs are seen (for each change in precision).

#include <iostream>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <random>
#include <boost/random.hpp>
    
typedef boost::multiprecision::cpp_dec_float<350> mp_backend; // <--- change me
typedef boost::multiprecision::number<mp_backend, boost::multiprecision::et_off> big_float; 
typedef boost::random::independent_bits_engine<boost::mt19937, std::numeric_limits<big_float>::digits, boost::multiprecision::cpp_int> generator;


int main()
{
    std::cout << std::setprecision(std::numeric_limits<big_float>::digits10) << std::showpoint;
    auto ur = boost::random::uniform_real_distribution<big_float>(big_float(0), big_float(1));
    generator gen = generator(42); // fixed seed
    std::cout << ur(gen) << std::endl;
    return 0;
}

Seems reasonable I guess. But how do I make it so that for n digits of precision, a fixed seed will produce a number x which is equivalent to y within n digits where y is defined for n+1 digits? e.g.

x = 0.213099234     // n = 9
y = 0.2130992347    // n = 10
...