Dear Conrad,
I finally had a chance to read all three of your FQXi essays and found that many of the themes you address are also those that I have spent time thinking and writing papers about. To just name two examples, on the issues of the context-dependence of "measurements" of physical quantities you may find this paper interesting, which deals exclusively with the measurement of time and space in special relativity:
http://fqxi.org/community/forum/topic/577
And with respect to the fact that all physical quantities derive their "meaning" from their relation to everything else in the semantic web of physics, you may find this paper interesting, in which the realization that the relationship of mass to the rest of the theory within the context of QM and GR is different leads to the proposition that mass in GR and mass in QM are two different quantities:
http://deepblue.lib.umich.edu/handle/2027.42/87999
But now on to some specific points in your paper:
You make a number of perspicacious observations, in particular, the fact that in physics all quantities are defined in terms of each other, that above and beyond the mathematical structure of our physical theories there is also a semantic structure layered on top, and the fact that there are very specific mathematical structures which exhibit a particular kind of interdependence is in need of explanation are important issues I have not seen raised elsewhere but can relate to very well.
For example, it bothers me when a high energy physicist says something like "we understand" such-and-such phenomenon (say, some symmetry like U(1) or SU(2)) because it betrays such an ignorance of the semantic layer (Feynman was a notable exception to this). On the other hand, I have been told by other physicists that my emphasis on what things "mean" in physics is more appropriate for philosophy than for physics. I personally strongly disagree with this point because I believe that only when we understand what things "mean" can we make theoretical progress in the absence of corresponding empirical progress. In other words, in the age in which the cost of building new experiments which probe nature at its deepest have become nearly prohibitive, the importance of understanding the "meaning" behind our fundamental theories was never greater than it is now.
I hope that the questions you ask will be considered by more physicists because the ratio of their visibility in discourse to their importance is extremely low.
Best wishes,
Armin