Dux,
The answer is simple yet complex. You don't need physical stamina and endurance. Learn the art of focusing your concentration on demand. You really only need to be able to focus your concentration for about 60 seconds. You should be able to do that even if you are physically tired. Often, I will shoot better when I am tired, because it keeps my conscious mind out of the way. I can't tell you the techniques here because it would take way too much space, but I can give you an idea.
Once you have learned how to focus your concentration, use key trigger words to get into the "zone". Use those words just before each stage. Until then, don't think about the match. Have a normal day. I used to man my sponsor's booth at the Nationals in between stages, sellling or talking to people. I didn't think about the match. About 10 minutes before the next stage, I would grab my gear, go to the safety area and gear up. Then I had a routine that I would use to get in the zone. Again, too lengthy an explanation for here.
After the stage was over, I would unfocus my concentration. The rest of the time, every match was a social event.
Many shooters tend to focus on the match for too long until it becomes bigger than they are. You know your ability, you know you are competent, so be that. Don't think about the last stage and don't think about the next stage - they are what they are, you can't change that. Have fun until it is time to shoot, then become a shooting machine.
Pm me and I would be happy to go into more detail or recommend some products that will help.