I don't have livestock either. I was bbq'ng the other nite and we were surrounded by flies. I was busy with the fly swatter. I cheat a little though. I spray them with soapy water (slows 'em down) and then I start swatting! A fly trap is a good idea. Fortunately, the flies aren't that bad most of the time, but sit down at the patio table to eat...and they all show up!
fly tape hung in strategic locations is somewhat effective too. I think the key is to be getting them all the time, not just when you are out there. an overall reduction in the fly population is the best strategy.
This would me more elegant, in my humble opinion, using flour and sourdough starter rather than sugar and active dry yeast. As the instructions mention, it works by emitting CO2 (I think moisture helps, too), should draw other biting insects. And having dead insects in it will eventually attract carrion seekers.
A bat box might also be worth considering, if there's a species that would do well there.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.