The G-code equivalent of the “speed button” is “M220 Sxx” where xx is “percent speed”. So “M220 S50” will mimic the “Quiet” setting at 50% speed. I think if you’re after quality more than silence, “M220 S90” will probably go a long way while not slowing the print down too much.
I would put it as the last line in the Machine Start G-code. If you want it earlier, you need to ensure you put it after the existing “M220 S100 ;Reset Feedrate” - or simply edit that very line (it’s line 19 in the Machine Start G-code for X1C in latest BS beta).