Furthermore your proposed remedy isn't even consistent with your biases, as you propose throwing $840 per house per ad infitum will make the complaints go away, and then turn and round and effectively say that nothing would placate them.
I'm sorry, but that doesn't make any sense at all. If nothing will placate them, then any dollar spent is wasted. If concern is warranted, then spending the money to actually solve the problem would be cheaper over the long term.
It's basically greed mixed with selfishness - deny the community improvement for the sake of my portfolio. So, if it's money they care about, then throw money at them. There's a break-even point, of course, where the bribe exceeds the benefit of the improvement.
You'll notice that I never suggested that improving the buildings was mutually exclusive with paying them off. Do both! Make the buildings quieter or less allergenic: try to address the complaint de jour. However, realize that you're treating a symptom, not a cause.