I found a somewhat better alternative than Bön suggests.
If you switch to the layout mode and set your pivot point to be "3D Cursor" then you can
shift-rmb move it around while you're in the sculpt mode:
An obvious benefit is that it preserves the mask, as opposed to the
Unfortunately, it's not as precise and you can only place the pivot on the surface (which might be enough for the simple moves/rotations). I looked around blender market and experimented with "Pivot Transform", which kinda works – you can get the pivot gizmo on screen via a hotkey, but it won't preserve the sculpt mode and will kick you out into the object mode after you're done (you can get back with
ctrl-tab, though). The combination of the two gets you really close to that popular sculpting software and its gizmo.