removal of blackman harris window results in signal higher than expected
The reason for that is that you don't normalize the DFT samples properly. Dividing by number of samples in time domain is valid only for Rectangular Window. For simple case of DFT, you should divide your amplitude by sum of window samples:

$$S=\sum_{i=0}^{N-1}w_i $$ 

This for Rectangular Window will be obviously equal to $N$ ($8192$ in your case), whereas for Blackman-Harris Window it's about $2939$, therefore the Coherent Gain is about $0.36$ instead of $1$. 

For reading more about this interesting topic I recommend you these papers (especially the first one):


  G. Heinzel et al - Spectrum and spectral density estimation by the
  DFT, including a comprehensive list of window functions and some new
  flat-top windows - especially chapter 9
  
  F. J. Harris - On the Use of Windows for Harmonic Analysis with the
  Discrete Fourier
  Transform