Don't your Regs say you must be fit for duty? If so, if you are tired get off. Fixes problems around here.
I guess the fear of the sack is the major impediment to the above but if your master has that attitude and you consider yourself a professional then do you really want to be there?
It's your licence, if you muck up and lose it see how long they'll want you around.
Unsafe is unsafe and we are our own worst enemies with this "press on itis" attitude. Draw the line and toe it.