Thanks, that's helpful. I would say that I largely agree with you, with some caveats. Grammar and syntax is the "objective" base from which we begin, certainly, but even they are not always as objective as we like. Greek is a real language, and like all languages, has ambiguities and difficulties form time to time. Part of the problem with many modern exegetes is that they haven't really learned the language as a language, but see it rather as a means of decoding meaning into English primarily to help with certain exegetical and theological questions. Particularly as you get into the more advanced stages of any language, grammar and syntax can become quite thorny indeed...
And context. Context is in part determined by vocabulary selection, grammar and syntax but these things are also determined by context, in that the speaker/writer determines what he wants to say because of the context, and it is context which then clarifies our understanding of what he is attempting to communicate. I think I know what you mean by the subjective nature of context claims, in that sometimes what seem to be crystal clear statements of Scripture will be challenged because of context -- questions of "women's ordination" are rife with this sort of thing in some circles, but we see it elsewhere as well. It also helps to define what we mean by context. There is a difference between local context -- the sentence and discourse immediately preceding and following the text in question, the larger context, the more extended discourse leading up to the text, and what is sometimes called co-text, documents by the same author and other related literature. Then there is historical and cultural context, which can illumine our meaning of the implications of a text. Done properly the last should enrich our understanding and therefore our application of Scripture, but at the same time it shouldn't override the "plain sense."
We can never wholly, I think, eliminate the subjective element in interpretation. We are, after all, subjects who involve ourselves in the process, and we can't eliminate ourselves. What we can do is test and retest our interpretations against the text in order to be as objective as possible, but always with the possibility that we could revise our understanding at some point.
I think I'm okay with "axioms." I resist when people start calling it things like "the laws of hermeneutics." More like guidelines, I should say. It's as much art as science.
Anyway, just some random thoughts inspired by your comments.