How do I remove specular reflection from metal and plastic glasses product photos?

I. You can not remove EVERY specular reflection.

Light bounces, that comes with the concept of Photo-graphy.

Imagine you are taking a photo of a mirror, eliminating every reflection would mean every mirror will be pitch black. That can only be made on a computer-generated image. The same would apply to a chrome metal lens frame. It would be black.

II. There is no way of removing reflections on metallic surfaces.

Because light is not polarized, so there is no way to block using any polarizing filter.

III. Reflections are part of what makes a product shot beautiful

Especially on glossy materials. Imagine a photo of a car without reflections...

You need to learn how to make those reflections a beautiful part of the photo.

Reflections give shape to forms, it gives you a clue if a shape is flat or curved.

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Sayed that:

You could use some method of multi-exposure

Moving the lights around, in controlled angles, and using the non reflected zones of each photo.

Take (at least) two shoots with the camera mounted on a tripod.

Prepare a setup with two sets of lights than can be turned on and off using different switches, you can simply plug and unplug set 1 and set 2 of continuos lights (you said "of the light bulbs themselves as tiny spots") or using different groups if you are using flashes.

Then you can stack them and use "if darker" blending mode.