I will touch on the results that I have obtained which can pickup Fine Structure Constant (FSC) automatically. Even in my system which I believe it to be fundamental the FSC is a maddening number, its like a water in an ocean it is everywhere but when you try to catch it it seeps through your hand

FSC alpha=.007297352568 , 1/alpha= 137.0359991 almost 137.036

so the trick that I could use and came naturally is to simulate and obtain two curves that crossed each other and when solved it gave an approximate value for FSC using wolfram alpha. of course I have simulation so the curves are constructed by curve fitting resultant points. So the data can be fit to multiple appropriate curves but non of them can give high accuracy because the simulation is based on PRNG and

**no matter how much iteration or number of point you make still you get errors** due to simulation and curve fitting accuracy.

example

https://www.wolframalpha.com/input?i=solve y=x^2, y=397.1161/x+549*exp(-19.57724/x) for x,y
https://www.wolframalpha.com/input?i=solve y=12.0163*x-3.18925, y=1.00*x^2 for x,y
and its final result

https://www.wolframalpha.com/input?i=(13801296569 + 120163 sqrt(13163446569))/200000000&assumption="ClashPrefs" -> {"Math"}
Note I am using the pro version if you have a problem but I think it is not a problem to use it with the free version. please tell me if you have a problem it can be overcome.