Dear Michael,
I just finished reading your essay. All three of your "what if's" are worth taking seriously, and I have read about a number of similar ideas that have already found their way into important existing work. A few thoughts come to mind:
1. As I'm sure you know, a vast amount of work has been done on the subject of "frequency analysis" in physics, signal processing, etc. As you point out, the "naturality" of the "time viewpoint" versus the "frequency viewpoint" depends on the system one is trying to describe. Something like a sine wave, which is described by a single number in frequency space, involves an uncountable number of values in time space.
2. Regarding "distribution" dimensions, as you call them, this seems very close to what is called "momentum space" in quantum field theory and other areas of physics. Three-dimensional momentum space is the space of all "wave vectors," which have units of 1/d, just like you suggest.
3. It's interesting to think about things like Newton's first law in this context. In antiquity, it was believed that a body in motion would stop moving unless one continued to supply a force. Of course, this turned out to be false... but not in momentum space! Constant "motion" in momentum space means constantly changing momentum. Newton's second law says that force is the time derivative of momentum, so if the force disappears, the momentum ceases to change! If the ancients had worked in momentum space, their intuition would have been right.
4. Turning to your second "what if," the importance of scale is still underappreciated in physics, in my opinion. You are quite right to point out the curious way in which different types of interactions dominate on different scales. There are at least five different domains where different interactions hold sway: the weak/strong domain, the electromagnetic domain, the gravitational domain, the dark matter domain, and the dark energy domain. Since this is as far as we can see in either direction (small or large), there is no reason to believe there are not further fundamentally different domains at even smaller and larger scales, just as you imply. I discuss this a bit more in my essay here.
5. Regarding your third "what if," Donatello Dolce has written an essay (in this contest) that you might find interesting. He discusses "elementary time cycles," and makes some bold predictions which would be very interesting if they turned out to be true.
6. I also looked at your essay about relational behavior. As you can see from my essay, this is a topic of great interest to me. I can't remark any further at the moment, but you raise some interesting points. This is also related to the "top-down" or "contextual" causation that is the subject of several essays in this contest.
Thanks for the interesting read, and good luck in the contest! Take care,
Ben Dribus