Any spec of dust or lint on the inside of the lens or in the cavity can show up as a visible defect in all of your video or images. This work would be best performed in a clean-room, but you don't have one.

Choose a room with dust-free air. Gravity removes dust from still air. Filters remove dust from moving air. Probably not the same location where you had the Dremel tool...

Use cotton balls, rubbing alcohol, or similar to thoroughly clean all dust and deposits from a 2' x 2' sealed/smooth work surface

Clean the cavity of the camera with alcohol and a fresh Q-tip and place it upside down to dry.

Open the new lens and clean the inside with alcohol and a fresh Q-tip and place it upside down to dry.

If the Q-tip is depositing any lint, then open a packaged lint-free lens wipe and clean the camera sensor window and inside the new lens.