Power spectral density of sigma-delta modulator
Everything you have written sounds correct so I assume you forgot to consider the BW for each FFT bin and are comparing to an expected spectral density that is per Hz.  Without windowing or zero padding the BW in each bin will be 1/T where T is the time length of your signal (so in other words 1 bin wide).  Therefore you want to reduce the total power measured in each bin by 10Log(1/T) to get the equivalent power per Hz spectral density.

If you are using windows you can refer to fred harris' classis paper on windowing for the Equivalent Noise BW of all common bins as well as windowing implementation loss for an accurate computation.

https://www.utdallas.edu/~cpb021000/EE%204361/Great%20DSP%20Papers/Harris%20on%20Windows.pdf