Well of course now I have to poke at my DAW (Logic Pro X) and see what it is going to do. I can't seem to find the keyboard commands to raise/lower level in 1 dB increments or .1 dB increments (Studio One - option arrow and shift option arrow), I can't make my faders "really tall" like in Studio One, but at least I can put the fader into exponential display which gives finer adjustment of the faders around unity. I can get finer control of the fader if I hold down shift while moving with the mouse.
I can change levels by typing them in, both for the VCA and tracks. I can enter volume automation values by hand. I also get the added bonus of fader changes now being "undo-able"
In Logic if I change level by .1 dB anywhere, VCA, track I get a .1 dB change in output level. Personally I can't actually make a 1 dB change using a fader very easily either on screen or using my X-Touch (Mackie Control clone) but I'm getting better.
Maybe using the keyboard arrows might do the trick for you?