That where timing is essential.
The key to any fight scene is fluidity. The movements between who's fighting need to be constant and spontaneous. The only real reason there should be any stalled movements is if there is some sort of dialogue going on or some plot device purpose. But for the most part, you're going to have to monitor yourself on this to which I'd also question is someone in your group an expert choreographer or perhaps a martial artist?
Another key thing and the most important is to exaggerate your movements.
But what do you mean by stunts that look phony?
When in doubt, just take the next small step.
With that next step take a deep breath. It calms the mind.
When the mind is calm you realize the best is still yet to come.