wireheading is wireheading, and it has a rather clear, explicit meaning

We've assumed that it has a clear, explicit meaning, but I don't think that's so.

here's real substance to the idea that we have some innate, true sense of desires, yet whose identities elude us.

In baseline humans and with current technology, yes, it does make sense to use the expression "true desire". Not that particular desires would be any more "true" than others, but there may be some unrealized desires which, if fulfilled, would lead to the person becoming happier than if those desires weren't fulfilled. As technology increases, that distinction becomes less meaningful, as we become capable of rebuilding our minds and transforming any desire to such a "true desire".

If you wanted to keep the distinction even with improving technology, you'd define some class of alterations which are "acceptable" and some which aren't. "True desires" would then be any wants that could be promoted to such a status using "acceptable" means. Wei Dai started compiling one possible list of such acceptable alterations.