Ideas:
- Drive-by mining: you probably have gas and a good vehicle by now. Do a rotation where you mine with the auger for a minute at one mining site, and then drive to the next site before the first site gets too hot. You'll leave before the screamers arrive, or if not, you'll leave the screamer horde in the dust.
- Stealth mining: wear a stealthy outfit while mining. It won't stop the screamers from coming, but they only scream if they see you. Keep an ear out for the first sign of a screamer, and pick them off before they see you.
- Active defenses: if you're going to have a big, conspicuous mining operation, you need to protect it. Install traps, even powered traps, at the entrance/perimeter to obliterate anything that comes to investigate what you're doing.