You can use the keypad arrows to move them pixel by pixel, and that is the most precise you can get. Although that last little shift by 1 pixel in your GIF...there's nothing you can do about it. Internally, the game doesn't store your screen co-ordinates, but a set of converted ratios relative to an internal display plane. So there are no nice whole numbers in the HUD config data, but lots of ratios that get converted back to actual screen pixel co-ordinates.

(PS: this is info I gathered during beta stage when the HUD config files were all pure text.)