I. As you say, "continuous light softboxes" It is most likely you are using fluorescent bulbs inside, that, normally have a green tint and not a good CRI.

II. You probably need to clarify (to yourself) if the problem is the covers or the light source (or both).

To do it: Using the same light at the same power, put in front of it one of the white diffusive materials.

Take a picture with a "sun" white balance. Leave the histogram in the middle (the exposition).

Now, change the material and take a second photo. Compare them.

You can do that now by switching light sources and using the same white material on two shots.

III. If you find out that the lightbulbs are the problem, you could try finding a socket threaded led light with a good CRI (Over 90-95) that fits inside your softboxes.

IV. You can also use a magenta gel to cancel the green tint. But the truth is that it is hard to determine the grade of the magenta tint you need. You could buy the softer magenta gel you can find, and put two layers if needed.

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V. But another option is to forget trying to exactly balance them, and use them in more creative ways, for example adding blue gels and using them on the background to make a teal and blue image, or adding an orange color to make them like a sunset color.