I use Vatsim for my ATC so I don’t need the build in ATC from Asobo.
I disabled the audio for the default ATC in the options.
If you press Shift-P for your pushback to start and then open the default ATC menu. You can request to steer to left or right. Because the audio is set to OFF this goes much faster and you don’t have to wait for a respons from ATC.
Still not perfect but it goes much smoother then with Audio ON