In case somebody, four years from now, has this same problem, I found a DECENT solution.
In the viewport, along the upper-right edge, it gives you the option to fine-tune “grid snapping”. Long story short, that’s the increments by which the object will move when you grab an arrow within the viewport and move it. The default is 10, and it goes as low as one. If you need anything finer than that, and you’re manipulating the object in local space, you’re out of luck. Inputing numeric values in the transform panel of the details menu only calculates for world space. This grid-snapping can also be adjusted for rotation and scale in that same area along the upper-right.