It's worth remembering that the word posh, is not posh.
This is not unrelated to the fact that many Latinate and polysyllabic words are less "posh" than some Anglo-Saxon (or at least Germanic) shorter words.
The case of lavatory is now a clichéd example. The cliché goes that the posh person says toilet, the uncouth person says bog, jacks, lav or various other slang terms from the euphemistic to the vividly vulgar, but the person who wants to appear posh uses lavatory thinking the longest Latin-derived word must be the "posh" one, and so reveals themselves as non-U (U being a term for posh that was coined by Nancy Mitford, and therefore much posher than posh though there was always a degree of irony in its use that is almost complete in its very rare occurrences today). Use of military slang terms like the head (Navy slang) might indicate more about past service than social background.
Other cases where the shorter and/or Anglo-Saxon was considered the posher by those too posh to say posh, are bike rather than cycle [both are of course contractions of the same word, but the former sounds more Anglo-Saxon as well as being shorter, and the latter reveals the Greek origin and matches another Latinate word], scent rather than perfume, false teeth rather than dentures, die rather than pass on, mad rather than mental, jam father than preserve, rich rather than wealthy, and what? rather than pardon? if you haven't heard clearly sorry rather than pardon if you have been clumsy and silence rather than pardon if your digestion has made its presence known.
These distinctions are no longer as they were, with examples of either (along with cases where it was indeed the longer or Latinate form that was considered U over a Saxon form considered non-U) becoming more common across all classes, for a variety of reasons.
You may have already noted that some of the U terms would also be those more commonly used by the working class; for example jam rather than preserve. This could suggest a middle-class affectation of a Latinate lengthier term to deliberately appear "posh" - the upper-class had less need to appear posh, since they were recognised as such already unlike the rising middle class.
There is a similar tendency toward euphemism among many of the non-U terms, avoiding die and mad where the upper-class had no such qualms.
A lot reflect a deliberate attempt to talk in a formal register on the part of the middle class. The idea that it is posher to talk in a more formal register is not entirely accurate, though not entirely inaccurate either - a deeper education makes a wider vocabulary and greater fluency available, making for differences both in how people talk informally and the ease with which they can use more formal registers. To non-U ears U speech is more formal, and to affect it one speaks formally. From this we have such fictional examples as the aunt in Brian Friel's "Philadelphia, Here I Come" who would say desist in case of stop despite the fact that while the former is undoubtedly more formal, the latter was the appropriate word and desist jarred.
Of the examples given in the question, expectorate and osculate stand out as comparable. They may have advantages of precision in some technical cases perhaps, but otherwise they have no benefit over spit and kiss, and are considerably less vivid. Unless one was stretching into formality for comic effect, they would mark one not as being posh, but rather of trying to appear so.