If you look at the signal level in whatever bus (or direct out) you’re using to record you’ll probably find that there’s too much headroom. The USB record only uses 16 bits and if you’re throwing away 30 dB at the upper end of the scale then you’ve esssentially got 11 bits you’re using to record (6 dB per bit) at which point quantization noise might start to be audible.
The best thing to do is try to rework your gain structure (turn down the main PA level so you can run the inputs hotter) to get the signal level higher in the desk. I don’t know if the USB record send is pre- or post-fade but you might want to check if changing the master fader on your record mix changes the recorded level at all.
One idea I haven’t tried but might work: set up your recording path as something like inputs->aux->matrix, with the matrix then sent to the USB drive. Send your inputs at +10 dB into the aux, the aux at +10 dB to the matrix, and then if necessary use the gain in the compressors for the aux and matrix to boost the signal further (set the threshold as high as it goes so the compressor never actually compresses).