Tensorflow: Convert Tensor to numpy array WITHOUT .eval() or sess.run()

The fact that you say "already have a session running" implies a misunderstanding of what sess.run() actually does.

If you have a tf.Session() initiated, you should be able to use it to retrieve any tensor using sess.run(). If you need to retrieve a variable or constant tensor this is very straight forward.

value = sess.run(tensor_to_retrieve)

If the tensor is the result of operations on placeholder tensors, you will need to pass them in with feed_dict.

value = sess.run(tensor, feed_dict={input_placeholder: input_value})

There is nothing preventing you from calling sess.run() more than once.