The only way of determining a number of minting shares would be to make a projection based on the own minting rate, but I doubt this can be accurate.
Assuming that the annual reward is approximately 2% no matter how many NSR mint, you can try to project the amount of total NSR minting based on that number.
With a total of ~1,000,000,000 (10⁹) NSR and ~2% of that being ~20,000,000 (2*10⁷) you can assume a daily generation of 55,000 NSR.
If you know how many NSR you have (say 5,000,000) and know how much you mint daily (say 825 NSR) you can calculate how many NSR mint.
In this example you have a share of 0.5% of all NSR and can expect to mint 275 NSR daily. If you mint 825 daily the minting ratio is 275/825=1/3
So you can assume that one third of all NSR mint, which would be 1/3 of 10⁹ and equals to 333,333,333.
But as this is based on some assumptions and not very accurate due to the minimum age to mint of 7 days (which is also the case for NSR having minted), this can only be a rough estimation.
Being able to interpret the value of the difficulty should be much more accurate, but I doubt that it's worth digging in the code for that.
@mhps did you calculate in a way similar to the one I lined out? Did you assume an annual interest of 1% or 2%?
...calculating with 1% instead of 2% could explain the difference of factor 2 between your calculations and @JordanLee's observations!