Hi Sergio,
I agree with your basic premise(I have rated you good). Moreover, I show in my essay what you wonder about. Also because you are a programmer my system is very well suited to your ideas.
Please if you have the time run The programs which are at my website
http://www.qsa.netne.net
please make sure you unzip the file properly, the code is in JavaScript, the programs are very simple. also see the posts in my thread for some more info.
you can find my essay at this link
http://fqxi.org/community/forum/topic/1877
see the amazing formulas in section 6, like this one
alpha/FSC =.007297352568, charge ^2=3, 27=3^3, m_e, m_p are electron and proton mass
M_p/m_e= (27/2)*(1/(alpha) -1) -1/3 = 1836.152654
P.S. you mentioned Khwarizmi
http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB
he lived one hour flight from my ancestral home in Iran.
Adel