Dear Conrad,
I appreciate the kind remarks. You make several distinct and important points, so let me itemize my reply.
1. Regarding the general theory of observation and its importance, my impression is that one reason why it is often neglected even in new theories is simply because the problem is so difficult, and is in some ways unlike the types of problems that physicists and mathematicians are used to solving. This remains true in spite of the attention the "quantum measurement problem" has received over the last generation. I am somewhat guilty of this myself; in my "secret papers" I have written down a lot of thoughts about this subject, but haven't felt sufficiently justified or confident to say much about it publicly.
2. I am glad you alerted me to the presence of your essay; I have read a fair number of them, but I am sure there are many good ones that have escaped my notice. I will be sure to read yours carefully. I think I agree with what you said in the paragraph above, but I hope to be able to say more after reading it. Let me repeat that I regard the problem as very difficult, however.
3. One of the aspects of the manifold assumption that bothers me is precisely that it postulates an entity that cannot possibly be observed, even with arbitrarily advanced technology. However, what bothers me even more is the extremely special structure ("too good to be true"), which makes the mathematics convenient at the expense of assuming a number of properties (least upper bound property? nonmeasurable subsets?!?) that seem obviously irrelevant to physics. In my mathematical work, I spend a lot of time studying things like complex manifolds and algebraic schemes, which constantly reminds me how very special, uniform, and "idealistic" such mathematical objects are. I get the impression that many physics students still get the impression that the shifts of paradigm from Euclidean spacetime to Minkowski spacetime to Riemannian manifolds represent vast and perhaps final generalizations of what is possible, when in fact all these constructs are perched on a tiny ledge over a vast gulf of models that might be relevant at much smaller scales.
4. I think that your expectation that the observable world "has to be based on several essentially distinct types of interaction-structure" is perfectly reasonable; indeed, it appears this way at ordinary scales, and the radical position, requiring the greater justification, is to assume otherwise. However, there are hints that a simpler picture might be possible. We seem to observe one arrow of time, not several, and to the extent that the arrow of time can be identified with the direction between cause and effect, it seems reasonable to ascribe causality to a single binary relation. If "essentially distinct types of interaction-structure" correspond to multiple distinct binary relations, then from this point of view you would expect "multiple time dimensions," which seems dubious, at least to me. There are several ways in which this chain of reasoning could be wrong, however.
In any case, I won't remark further on this until I have read your essay! Take care,
Ben