This is a nice and thoughtful post and I agree mostly. I'd like to add that my use of the word "Castilian" reflects my experience of usage of the term here in Barcelona (when speaking "Spanish", Catalan, and English). It's not a hard rule of course, but people are especially likely to refer to Castille over Hispania when distinguishing from other languages spoken historically within the country.
The term also usefully refers to the prestige dialect of Spanish, as might be spoken in Madrid. This is useful to distinguish from e.g. the "al-andalus" (Andalusian) spoken in the south which is more treated as a dialect than a separate language (though the distinction is of course fuzzy).
(On the other hand Barcelona in particular has a significant population of sudamericanos who will usually say "español", certainly that term is well used and understood.)
The term also usefully refers to the prestige dialect of Spanish, as might be spoken in Madrid. This is useful to distinguish from e.g. the "al-andalus" (Andalusian) spoken in the south which is more treated as a dialect than a separate language (though the distinction is of course fuzzy).
(On the other hand Barcelona in particular has a significant population of sudamericanos who will usually say "español", certainly that term is well used and understood.)