Just a low v2 (rightclick, create v2 cloudlayer) cloud layer would do, say 100m high, set at 45m altitude, with a smallish cloud fractal and enough density. Thin the cloud density to a subtle mist. That may need some experimentation, as you say it's either too thick or too thin. Taper top and base can be unchecked for full height of the layer, especially if your camera is within it.
To avoid grain, I'd set quality to one and if needed in render settings customise sampling (if using AA6, you could set it to 0.03). Do show us what you accomplish!
