How to apply a single fully connected layer to each point in an image
What you're describing is a 1x1 convolution with output depth 1. You can implement it just as you implement the rest of the convolution layers. You might want to apply tf.squeeze afterwards to remove the depth, which should have size 1.
I'm trying to set up a non-conventional neural network using keras, and am having trouble efficiently setting this up. 
The first few layers are standard convolutional layers, and the output of these have d channels, which each have image shapes of n x n.
What I want to do is use a single dense layer to map this d x n x n tensor onto a single image of size n x n. I want to define a single dense layer, with input size d, and output size 1, and apply this function to each "pixel" on the input (with the inputs taken depthwise across channels). 
So far, I have not found a efficient solution to this. I have tried first defining a fully connected layer, then looping over each "pixel" in the input, however this takes many hours to initialize the model, and I am worried that it will slow down backprop, as the computations are likely not properly parallelized.
Is there an efficient way to do this?