Yes — the black images are because 1/16000 is far too fast for your lighting, so the sensor isn’t getting enough light. The guide meant that fast shutter speeds help freeze motion, not that you should always use the fastest setting.

For paintings on a tripod, the subject is not moving, so you can use a much slower shutter speed.

A practical approach:

• Use low ISO, around 100–200; raise to 400 only if needed.
• Use an aperture around f/5.6 to f/8.
• Let shutter speed be whatever gives correct exposure: in aperture priority, the camera can choose it automatically.
• Once you find a good exposure, you can switch to manual and keep the same settings for the whole series if the lighting stays constant.
• Keep using the tripod; a remote release helps avoid shake.

Also pay attention to setup:

• Make sure lighting is even across the painting.
• Place lights far enough away and symmetrically to reduce brightness falloff.
• Keep the camera exactly parallel/perpendicular to the artwork so the painting stays rectangular.
• A gray card shot can help with later color and exposure correction.

Your camera’s slower automatic shutter speeds are expected here.