If you're able to get a sample to photograph without squishing the fly too badly (probably not easy, we acknowledge), we can try to ID it. Several kinds of flies aside from mosquitoes can bite, so it's hard to say. All require damp substrates in which to breed, so like mosquitoes, eliminating sources of moisture (like puddling water after heavy rain in areas where the soil doesn't drain well) might help to reduce their population going forward. If you're near a natural habitat where moist areas support the fly population, then unfortunately there isn't much that can be done except to use personal repellent (the same kinds that work for mosquitoes should work on other biting flies). There is no pesticide for the adult flies that we would recommend using as such sprays would, as you noted, pose a risk to pollinators and other beneficial or harmless organisms, including insects and spiders that prey on flies. Fortunately, as we approach frosty weather in a few more weeks, the flies will soon be gone.

Miri