The ND filter technique will work ok until you start to stack them up, then the errors of their accuracy will start to appear.
Yes, place black behind the tube. And try measuring the "patches" with a spot meter to see if your scale is accurate enough. Don't be surprised to see color shifts as you stack the ND filters.
And also, the DR of the camera will be effected by the color temperature of the lamp. From my experience, maximum DR might be at a color temperature of 4500k, but each camera might be different. For practical reasons, conduct the test with "daylight" and "tungsten" lamps.
Also, the "base" ISO might not yield maximum DR. So do the test at varying ISO settings as well.
Now that I think about this, I have a better idea from my film testing days. I used to shoot movie film in my still camera for this test. Instead of trying to capture the whole DR in one image, I photographed a white towel exposing from below maximum black to above maximum white. I then placed the frame strip on a light table and looked at my new "DR ramp". Why the towel? The texture in the cloth helped to see where I lost visible detail.
How to do this with a digital camera? Shoot all your images of the white towel by varying the exposure in the camera. Then take one frame from each, crop it, and create your DR greyscale test ramp in video editing software such as Resolve. This way you will not rely on the ND gels, you'll be able to see where you loose detail in the texture of the towel, and you'll be able to have 1/2 stop exposure changes rather than the full stop changes that the ND gels provide. And you will also learn how to expose for your camera using a spot meter when you're actually shooting a movie with it!