Well Dr. Richard,
You may be catching on to the actual problem I am solving. I hope that is true as it would be great to be able to discuss the thing with some who can follow the math. Yes, in deedy do; that is in fact the key to the whole thing. You know as well as I do that a lot (and there are serious indications that the correct answer is all) of physics can be derived directly from symmetries. The difference between what I do and what has been done in the past is related directly to that word "assume".
As you have noticed, I take the position that the mechanism (called our senses) cannot be depended upon not to yield up illusions of symmetry (especially if those symmetries allow a simplification of what one must remember in order to survive; and what else pray tell are the laws of physics anyway). So I say one's analysis must allow for the possibility that all symmetries I can conceive of can be generated by that mechanism.
However, there is one complication here which must be carefully handled. Whereas if I assume a symmetry (as per standard physics) I need do no more than postulate a symmetry in my representative mathematics. Since the asymmetry is assumed, no need for justification of that symmetry is required (it is presumed to be a characteristic of reality). When the symmetry is generated by the mechanism processing the fundamental information obtained from reality, one has to at least have some idea how that mechanism can accomplish the particular illusion before one can deduce the consequences.
Now, shift symmetries are a very straight forward issue. I know exactly how such a change influences my data. As you say, Jeeva Anandan conceives of many different kinds of symmetries and, if one can express exactly how those particular symmetries would impact a totally undefined data set, then I am quite confident one could deduce the impact of those symmetries on the laws of physics. I will leave that problem to the young guys as I know my mental abilities are not a fraction of what they were forty years ago.
The two approaches to the idea of symmetries are quite different. For example, my approach implies that a scale shift symmetry (multiplication) is as necessary as is simple additive shift symmetry. But no common physicist would ever even think of "assuming" such a symmetry. It is just not something reasonable under his mental image of the universe.
I would also point out that gauge symmetries are symmetries in the mathematical representations of the laws, not in the base data itself. Which make them a somewhat different issue.
Essentially, I must allow for the possibility that all symmetries I can conceive of can be generated by that mechanism but I certainly have not deduced the consequences (or even figured out how to represent those other possible symmetries). Speaking of symmetries in mathematical representations, I can think of one which is quite trivial under the representation I have chosen: that would be the Fourier transform. That issue is trivial because the mathematical structure of quantum mechanics (which I end up deriving) is explicitly symmetric with regard to that change.
I am sure that much more can be done with my attack than what I have done. And, I always forgive ignorance as we are all ignorant in one way or another. What seems unforgivable to me is refusal to consider possibilities not supported by authority. That attitude is a dead end street.
Have fun -- Dick
PS I am going to post this to Astronomy.net Let me know if my doing that bothers you.