Dear Mr. Saunders:
Thank you for your very innovative essay.
I am not entirely sure that I understood everything correctly; however, it seems that you are taking different measures of time (as related to position, through velocity, and as related to entropy) and assigning them different dimensions. If I am correct, then I imagine that there are situations in which your ideas would be useful.
However, I think that there is a difference, between various measures of time and the dimensions of space. In general, there need not be a correlation between positions, along the different dimensions of space; but I think that there is always a correlation between all of the measures of time. Put another way, position, along any one spatial dimension, generally need not be a function of position, along any other; however, I think that any measure of time can always be stated as a function of any other measure of time. I am not totally sure about this, but I hope you find the thought useful.
Good luck in your further investigations.
Take care,
Ken.