I haven't really fully investigated the kernel-side of the profiler, but would it be possible for the profiler to consume the kernel's stacktrace buffer when you read from the /proc entry? This would allow for the Profiler application to "stream" new profiler information occasionally from the /proc/ file and allow the profiler to run for longer.

The process being profiled could also block until there is space in the stacktrace buffer so you don't miss out on any stack frames.

My idea is based on macOS's instruments application that shows graphs changing over time and you can see the information while profiling is occurring