I agree with your approach of counting letters and using their frequencies

About frequency of A/T/C/G agree again - but but I would much prefer to calculate it across ALL sequences, rather than just 1 sequence at a time - corresponding to one $ID, so that this frequency-compliant sequence randomization is based on global rather than local frequencies. I suspect it will result in even more reduced signal / noise ratio, though I have not tested that yet... Thank you!