How to reconstruct the image from a neural network output?
You can't necessarily use the output of a neural network to reconstruct the image, like you want.  The output signals indicate how the neural network has classified the input image.  Beyond that, they don't necessarily have any interpretation as a representation of the original image.  There isn't necessarily any way to do what you want (to reconstruct the image given the output of the neural network), as this kind of neural network inherently throws away information.

Are you familiar with the notion of training "autoencoders"?  One way to train multi-layer neural networks is by building a series of auto-encoders: e.g., to construct the weights for the first layer, you train a 2-layer autoencoder, then throw away the second layer of the autoencoder and use the first layer of the autoencoder as the first layer of your neural network.  You repeatedly do this for each layer of your network.  Autoencoders do reconstruct the original input, so if you're training each layer of the neural network in this way, then you automatically have a way to reconstruct (an approximation to) the original input from the signals at any layer -- if you saved the entire autoencoder at each stage.  However, if your real end goal is to understand why an image was classified a certain way or debug your neural network, I expect this probably won't be helpful for that.

I'm not 100% sure what your real goal is.  You mention "test each solution for fitness", but I'm not sure what you meant by that.  However, my guess is that your best bet will be to figure out what your real goal is, and then ask about how to achieve that goal (which might not be by trying to reconstruct the original image).