Ok I went back over and double checked everything yields similiar results even with the decimal range added into the math. However, I forked out the gil to do some more rigorous testing (which I should have probably done after figuring out the natural STR/Flat Mitigation Values) to get a precise reading using low/mid shields.

Maelstrom Shield = BS 6 = 13% mitigated
Square Ash Shield = BS 8 = 13% Mitigated
HQ Ironclad Bronze Buckler = BS 11 = 13% Mitigated
Vintage Square Shield = BS 12 = 14% (11.5)
Aubriest's Allegory = BS 22 = 14%
Vintage Hoplon = BS 23 = 15% (11.5)
Darklight Square Shield = BS 24 = 15%

Since my mitigation from STR and the 7% flat rate comes out to 13% I gain nothing from the first three shields block strength. However following the incremental values according to my theory we see that I gain 1% of mitigation at 12 BS and again at 23 (23 / 2 = 11.5) which falls precisely into my hypothesis at 11.5. I wanted to further test my theory on a shield with 34/35/36, BS but no shields are avaliable in close enough increments to properly test, however compared to other shields that were already tested at the higher levels it seems everything has panned out as I had hoped.