trip_signal() has another problem. If pending->finishing is non-zero, _PyEval_AddPendingCall() uses the C API whereas the current thread may not hold the GIL. That's forbidden by the C API.
The more I think about it, the more I think that pending->finishing is fragile and should be removed.
I understood that pending->finishing was added to workaround crashes during Python finalization. I fixed multiple crashes related to daemon threads during Python finalization in bpo-39877. Maybe the bugs that I fixed were the ones which pending->finishing was supposed to work around.