Many moons ago we had large numbers of sparrows around the property.
My father built a trap in the shape of an M ( viewed side on) at the botom of the M was a hole big enough for a sparrow and the rest was covered with spare chicken mesh. It would have been 2 M long and 1 M wide and about 750 mm high.
Bread was put inside and over the course of the day it got more bread added as the bird prison numbers increased. That was my job.
Getting on towards evening we had maybe a hundred birds in there.... could be more.
Dad got an old sheet / drop cloth and covered the cage.
Disconnected the garden hose from the tap and ran it from the car to the cage.
10 minutes of that and they were all dead!
Our Polish neighbors were a bit upset, they had numbers down the inside of their arms and had narrowly missed similar treatment.
Your idea has some merit but I would opt for cynogas ( lighter than air ) or Lavacide ( heavier than air ) as was used by pest boards back in the day.
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