hmmm. well i won't be of much help since i'm a "semiotic newbie" but perhaps Gecko or Staze can elaborate. meanwhile, i'll try to fake my way through a response in the interest of helping out...

i do know that in semiotics there are roughly two fields, those concerned with linguistics and those concerned with the nature of signs and sign computation.

between those, there is some introduction and argument of the ontology of semtiocs. peirce had published some categories of signs that start with a minimum of three and go up from there. others have elaborated adding more ontology / categoires - esp. the linguistics crowd. i think the strongest arguements i have heard are that three are all you need and that everything can be represented using three categories. peirce himself makes this argument so perhaps you can draw from it. these three are firstness, secondness and thirdness.

umberto eco and john sowa are two names already mentioned here that come to mind that may be of help. also, mentioned are sarbo and farkas who deal with peircean ontologies and language.

also, the sematic web is an exercise in ontology madness so perhaps there is something to glen from that effort and or Tim Berners-Lee

anwyay, perhaps the others will chime in...

I have no formal music background, so I can't specifically address the Schenker viewpoint (although I'd like to learn more). However, circularity is fact of life in any ontological or logical system (the dictionary on your desk is a prominent example of this) -- with a few caveats. Circularity can be "dealt with" by producing strictly hierarchical ontologies. Often times in practice, the highest levels of abstraction become escape valves, perhaps better thought of as kludges, to enable everything to fit supposedly nice and tidy in a particular world view. Only toy problems, or those related to extremely narrow domains can cleanly use strict hierarchical onologies ("only" is a little strong, but to make a point...)

An example of this is the toy ontology "animal, vegetable, mineral". Sure, we can fit most anything into these categories nicely. However, try to describe an animal, vegetable, or mineral within its own ontological system and you'll come up empty handed.

One angle to consider is to leverage Godel incompleteness and see where that leads. Of course this could be seen as the "bah humbug" approach, since it leaves any logical system open to attack. However, it's a way of thinking that may help narrow the focus on the slippery slope components of Schenkerian analysis. You may discover additional dent material exploring this sort of path.