Ditch the Sniper. Use the BR on Grunts only. Sword and Grenades for dealing with the Elites. There is also a Fuel Rod under the stairs.
Be very aggressive and kill as few enemies as possible. Resist the urge to kill everything. It's better to kill one Elite and have the rest chase you, than to kill 2 Elites and have another wave spawn.
Punch the Prophet and head to the side stage doorway of least resistance making sure the enemies see you go through the door to force them to follow. Sneak up the stairs and immediately jump the Prophet from the bridge. Try to time it so the enemies are in the stair well when you jump him. While punching the Prophet you can turn the camera to plan your escape route.
If you see more than 2 elites head outside so you can use dropped weapons to kill all but one of the Elites who follow. Then grab a fresh Sword from under the stairs on your way back in.
Most importantly, make sure Prophet Birthday Party skull is turned on.