At a job some years ago I got SMS messages from system monitoring almost continuously, around the clock. Most were spurious "this is an indicator that something might possibly go wrong" status messages, and I worked hard to smarten up the monitoring. Once I was only getting messages when something actually was going wrong, I worked hard to make the system more reliable so that I could get a good night's sleep. The more I continued down that path, the more time I had to make the system even more reliable and also add needed features.
This sort of approach is not limited to coding at all. It does require that you have some control over the issues that take up your time and energy. If your PM were to quit and you were to take up that position, I'd advise you to take an in-depth look at removing the problems that lead to frantic, urgent requests.
Most of them were due to an outage we had on a "legacy application" due to some sort of screwups with the VMs it was running on. This caused reps to hammer me with questions about our SLAs. Of course I had no answer.
Many more emails were from offshore devs from a project I'm not normally involved with who didn't understand our specs.
There were also a smattering of issues with reps getting calls that our app was down. Ask a few questions and it turns out the person is using it on a train in a tunnel in the middle of iowa type of situation. It's a web app.
This sort of approach is not limited to coding at all. It does require that you have some control over the issues that take up your time and energy. If your PM were to quit and you were to take up that position, I'd advise you to take an in-depth look at removing the problems that lead to frantic, urgent requests.