Is there room to remove the incandescent bulbs and put a single fluorescent tube in there? If it was a few inches behind the glass that might make the appearance to be more evenly lit. They make thin fluorescent tubes in different lengths, just need to add a couple of wires to get 115v to it, some of the fluorescent light tubes come with the power cord already attached. Also, there are diffuser panels made of milk-white plastic that can help even the lighting, it would install immediately behind the glass. I'm not familiar with your machine so don't know how much room there is behind the glass.
Another idea would be to try LED lamps in place of the incandescent bulbs, maybe there is an LED with diffuser lens that gives a softer & more scattered light. We had a piece of equipment at work that had little metal shields on the lamp holders half way around so that the light was reflected to the rear and then gave indirect lighting to the front, sort of like the "sconce" lighting fixtures. There were no bright spots on the glass from the lamp since there was no light going directly from the lamp forward. Below is a picture of a lamp shield used on some cars to give an idea what I'm talking about.