This thread reminds me of this other thread from a few weeks ago:
http://thephilosophyforum.com/discussion/534/is-intersubjectivity-metaphysically-conceivable/p1
There, somewhat similar to your OP, I reached a somewhat solipsistic looking conclusion, that one cannot ask as to whether or not other minds exist. I prefer your presentation of the basic problem to mine, although I think your conclusion is confused.
To recap and expand a little:
The logical inference of other minds is an inference that is made via a supposed analogy with one's own case. This inference is motivated by our natural empathetic instincts towards other people's behaviour that often cause us to identify our own feelings with the feelings of others.
Hence at first glance, the analogical inference of other minds in themselves might seem to be unquestionable and a forteriori, sensical. And there is also the fact that, as for instance in the case of pains, that we don't merely use our own personal pain-behaviour as an a priori model for understanding third person pain-behaviour, because we also use our understanding of third-person pain-behaviour as a means of understanding our own first-person pain-behaviour. For example, just after stubbing my toe i immediately begin to recognise this fact in a shared language, by recalling similar past instances of myself stubbing my toe and leaping around the room as if observing myself from a third person perspective, and comparing and conflating this memory with both my current predicament and all of the times I have witnessed others doing the same.
But is argument by analogy valid for interpreting other minds as things in themselves? I conclude not for precisely the reason you state, for the supposed analogy relating the first and the third person isn't an analogy at all; for an analogy to be an an analogy it must be restricted to external comparisons that are empirically sensible, as for instance, in comparing apples to oranges, or in comparing external behavioural observstions of myself to external behavioural observations of others, or in comparing the law of addition in Peano arithmetic to the law of addition in Robinson arithmetic (these are also empirical examples since they involve empirical comparison of use cases in different calculi).
However, in the current case, we have merely assumed that there is a first vs third person analogy via a superficial appeal to introspection that has already conflated the first person with the third person. But as previously argued, for introspection to present a logically valid argument by way of analogy, the analogy must be reducible to what is sensical from the perspective of the first person, or else be rejected as logically nonsensical, even if accepted as being emotionally meaningful.
Hence there isn't an analogy relating the first and third person after all, and therefore other minds in themselves are not logically conceivable. This conclusion looks a bit like epistemological solipsism, namely that one can only know of ones personal pains and remain agnostic about the pains of others. Yet this is also mistake, since neither can the ABSENCE of other minds be logically conceivable. We are merely left with sensations and feelings, including empathy and social harmony, that are not logically interpretable in terms of a public-private distinction. For this reason, if this is to be described as a solipsism it is a grammatical solipsism.
To quote Wittgenstein, "sensations are private" is comparable to "one plays patience with oneself", from which I conclude that "are" means 'analytically entail being'. So talk of public sensations, i.e third person sensations, is nonsense, ergo the notion of sensual privacy is also nonsense.