I feel for you
I really do. I used to feel compelled to constantly check/respond to emails off-hours. I thought it would give me job security. All it gave me was insomnia/weakened immune system. I also work for a large multi-national corporate meat grinder. The stress level is extremely high, there's always a fire that needs putting out.
My physical and mental health are far more important to me than whatever artificial goals are placed on my department by some bonus-oriented PHB.
Luckily my role is more sale related so no 24/7 on-call. Work phone gets shut off after hours because It doesn't matter what I type in any email when I'm not at the office, it will not change the fact that when I come in next business day it will always be EMERGENCY! URGENT!.