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This talk by Paul Ramsey mentions that there is a _ST_BestSRID function in PostGIS. I assume it exists to find the best projection when casting unprojected data for other uses.

I cannot find docs on this. Is it actually exposed, and if so, what are the parameters?

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Yes that is correct. The functions that start with _ are not documented because they are what we consider "private" functions, not for general consumption.

If you look at the functions with smiley faces on this page: http://postgis.net/docs/PostGIS_Special_Functions_Index.html#PostGIS_TypeFunctionMatrix

You will see they all use this _ST_BestSRID functions (and there are two forms of that function). The smiley is meant to say these are functions using a hack, and not using pure geodetic calculate.

Study the code behind the smiley face functions and it should be clear how to use _STBestSRID in all its forms.

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