Have you tried the runing rabbits on a sporting clays course? Those are a fair comparison to a running deer. They bounce up down while rolling broadside or at angles away from you at fast speed. Fun fun fun!!

Years ago I was doing alot of trap shooting.
One season I was hunting Blacktails on the island when on the last morning I jumped a spike buck out of the cover directly ahead of me and he was in full flite heading away and quartering to the right uphill. My instincts just took over and when my cross hairs passed thru his head I fired and took the top of his head right off. He was about 75yds away maybe a little further and my rifle was a .243 with a 4X scope. The whole thing was totally instinctual on my part and I never tried to conciously think out that shot.
I look back on that shot and wonder why I shot him in the head, I always said I would never do that. Guess it was to make sure he was legal.
Heck writing about that one reminded me of another ealier occasion, this time a doe, she took off across a large creek from me and I did the same thing with her. As the front sight bead went past her nose I fired and put a 170 gr 30-30 right thru her ears! She was closer only 40 yds I think and going squarely across.
I have never been one to try that very often and a few times at long range missed them cleanly. They can be a very difficult target when they are bouncing along thru a logging slash.
I guess I favour the instinctual pass thru the target and fire on the swing type of running shot.