Burning bushes are practically weeds around here. I don't know what to say. Three hours of watering? That's kinda nuts. Neighbor problems are unique and nasty. Is he an older gentleman? Don't know what to tell you. If it's a townhouse situation there should be an association or landlord to deal with these issues.

Build an obnoxious shield on the edge of your side that borders his, so when his sprinkler tries to squirt your bush, it repels the water back onto his side. I'm trying to think of a material you could use that won't look hideous, but I am drawing a blank. Perhaps a shower tiling board that is screwed\wire-tied into T-posts to hold it firm and anchored to the ground. I hope that wouldn't be an expensive endevour, but it might be what you need to do if so much as to get the neighbor to come to his senses or else he gets to look at your great wall for ever more.

This is causing the top leaves of my burning bush to turn reddish brown and curl.
Is it from the water hitting it for so long daily, or from drowning due to the soil being so wet? If it is the latter, you might try lifting the bush, and making like a mini raised bed, and replant it.
Is there any way you can just move it to another side of the property, or are you wanting where it is, to block him out a bit? If the latter is the case, you might consider planting some bamboo.

Sue