Instead of generating a perfect set of lights, which may be expensive, it should be possible to correct some uneven illumination via software post-processing.
One solution is to generate a static, white-field exposure of the space you wish to image. Essentially, drape the area you wish to image with something as close to perfectly white as possible, and then capture an image of the area with the same illumination setup you will use on whatever you wish to capture. The drape should be white and matte, i.e. not have specular (mirror-like) reflection, but instead have diffuse reflection, like paper or a cloth. Once you've captured the static, white-field image, you have captured all of the uneven-ness of your illumination setup. You can then subtract the uneven-ness from any future images to correct for uneven illumination.
A drawback to this method is that it works best with flat objects, as the illumination uneven-ness may change if a 3D object is inserted into the frame.
This Matlab tutorial gives a general idea of one way of correcting uneven illumination. Their method involves determining background illumination via software (which you can also do). Since you have access to your own hardware, you may also capture the background illumination as discussed above, and follow the remainder of the procedure.
Ideally, non-uniformities in illumination should still be minimized so as to ensure you capture as much information as possible through a wide-spread histogram distribution. If the illumination non-uniformities dominate the overall image lightness, then you aren't capturing as much lightness information from the objects in the frame.
Photography.SE may also be a useful source of information.
