I'm no photographer, but I have the same or similar problem trying to take photos of LED installations. I get a dim background and overexposed leds, consequently no colours. I think the problem is that the autoexposure adjusts for the average level, which is correct for neither on a high-contrast scene. Our eyes can cope with this by correctly exposing the segments and making the unlit parts invisible - which may not be what you want when illustrating, but works well for reading the values whilst obscuring the structure.
The answer is possibly to run them at low brightness and with plenty of incident light, so there is not so much difference in brightness between self-lit and incidently-lit parts.