Coornio's post in About blend modes and their code was marked as the answer
As is the usual after one posts a lengthy post requesting help, I managed to solve it with the help of another third party. For those curious:
weightSrc = Asrc / 255;
weightDst = 1 - weightSrc;
Aout = min(Adst * weightDst + Asrc, 255);
Rout = min(Rdst * weightDst + BLEND * weightSrc, 255);
Gout = min(Gdst * weightDst + BLEND * weightSrc, 255);
Bout = min(Bdst * weightDst + BLEND * weightSrc, 255);
// where BLEND stands for the particular blend operation you require,
// eg: Difference is: abs(Rsrc - Rdst)
// eg: Multiply is: (Rsrc * Rdst) / 255
// eg: Additive is: min(Rsrc + Rdst, 255)
// normal alpha blending in particular is easier
Aout = min(Adst * weightDst + Asrc, 255);
Rout = min(Rdst * weightDst + (Rsrc * Asrc) / 255, 255);
Gout = min(Gdst * weightDst + (Gsrc * Asrc) / 255, 255);
Bout = min(Bdst * weightDst + (Bsrc * Asrc) / 255, 255);
I am not 100% sure if I haven't made any mistakes, but some rudimentary testing through the color picker in a comparison between paint.NET's blend and mine shows practically identical values, minus rounding differences.
Coornio's post in About blend modes and their code was marked as the answer