What if we introduce new mode, activated with hotkey/button (pressed or toggle). In this mode shields are decoupled from aiming direction and left in its current position. When this mode is deactivated, shields return to the aiming direction with normal speed. Let's call it "Fix Shields" mode.
It could work both with mouse and gamepad. Also shields in this mode can be adjusted with two separate keys or buttons.
On the other hand, huge advantage in controlling the shields with mouse is the ability to quickly drop it and immediately raise in some other direction, including the opposite. (BTW from the lore viewpoint, it's a plain cheat.
If this can be achieved somehow with gamepad, it's a breakthrough.