The article, has a classical engineering approach (might be wrong I just skimmed it), not that it's a bad thing. The general criticism of bias against sparsely coding neurons is correct, don't know how they can say its a factor of 10 or anything else though.
Average firing rate of one neuron only makes sense in relation to a different condition. For example in sensory neuroscience studies, we say a neuron likes a stimulus if the average firing rate of this neuron while the stimulus is presented is higher than in an equal period in the absence of the that stimulus. Conversely a neuron dislikes a stimulus when the average firing rate goes down.
Average firing rate across all neurons also is a weird measure as neurons have different baseline firing, different morphologies, are part of different circuits and have different functions in these circuits. It would be like saying that the average of a normal distribution is enough to describe it ignoring its variance.
Regarding the question itself a couple of things should be better defined: what is higher order thought? and medium time planning of what?
Neurons certainly do not all fire at the same rate, however rate implies a time constant and most importantly when one averages across multiple neurons one must have a criterion of selecting them which begs the question: Which neurons? How does one defines an area of the brain? Morphologically? Functionally? Genetically? Furthermore, what is its relevant time constant? These seem like basic obvious questions however they don't seem to have a clear and defined answer yet.
You seem to have a particular architecture in mind with multiple areas that have different functions, I assume you are modeling it. All models are wrong (yeah yeah I know its a cliche) which is to say that every model has a particular set of more or less valid assumptions. You just have to know what these assumptions are and what you can conclude given these assumptions. So basically there isn't really an answer to your question from the biology side we're still blind scientists in a dark room looking for the brain dead cat that is hiding the light switch.
Once I figure out the function of an arbitrarily defined brain area I'll let you know its time constant, then again it is arbitrarily defined and I cannot possibly figure out its function in all possible conditions without having assumptions of my own of how things should work...