Hi, just to confirm that I am understanding, let me restate: you are setting enlarger exposure to just barely give a visual "black" on the print when exposing through a clear, unexposed piece of film. Then, when you use this same enlarger exposure with a real negative, the parts that should print black, or nearly so, actually print much lighter. (Do I have this correct?)
Additionally, when you read the film density of the desired black objects, you find that the film density is significantly higher than the clear film, by about 0.45 density units (which is quite a lot).
It seems to me that you have quite a lot more camera exposure than you need. These fairly dark areas are not much affected by development errors, so I disregard such possible issues. It seems pretty clear to me that you have overexposed the film, at least with respect to how you want the scene to print. Since you also came to this same conclusion, I'd just say that I agree with you.
Obviously the immediate solution is to increase enlarger exposure; I personally don't put too much emphasis on that "clear film to print black" exposure routine, so I wouldn't be caught in your conundrum.
If your real question is, how does this happen, I'd suggest three possibilities. First, you might have a poor metering technique (also, there might be a defect with either the meter or the camera shutter/aperture). Second, the scene may have produced a lot of flare light inside of the camera, similar to an overall "fog" on the film. Or third, it may have been an issue with the "color" of the hot lights. Such lights have low "blue" output and a great deal of "reddish" output. In this situation, even films with the same daylight ISO speed can require different camera exposures depending on how far their red sensitivity goes. I haven't looked up your film, but if it has an "extended red sensitivity," this is a possible factor.
If I were in your shoes, I'd double check my meter, either against another or vs a standard daylight exposure. Then I'd visually check the stop-down performance of the lens, as well as the range of shutter speeds. Then finally, in the new test shoot you are planning, I'd include a range of exposure tests. From those, I could pick a "best minimum exposure," and use that to estimate a new film speed rating that I would use only for this film combined with this light source.
Just my thoughts on the situation.