The point of the reference to boca de caballo (actually I first learned it from you some years ago but do not recall the source you gave)was to illustrate that the bilobate shells were certainly around LONG before the so called 1728 pattern. The Pappenheimer rapiers were similar in a sense as I described because of the shell position in the hilt configuration, and these were of course used during the Thirty Years war in Germany and its environs.
The name game is just that, and it is the obsession of collectors to appoint catchy names to certain weapon types, much in the way weapons are often nicknamed in military contexts colloquially.
The Pappenheimer appellation is of course referring to a commander of armies in the Thirty Years war who is presumed to have favored this design rapier.
With the 'bilbo' term, of course it too is a 'collectors' term, but seems to have deeper associations in use in Shakespeare's "Merry Wives of Windsor" where the term refers to a rapier with fine steel blade (Biscayan iron) so its use appears to extend to latter 16th c.
It is interesting to note that the term 'bilboes' also may refer to a bar of iron with sliding fetters attached, a kind of shackles used to hold prisoners etc and thought to refer to the city of Bilbao where these may have first been made. Perhaps this association of iron bars may be a visual association much as with the horses bridle bit (pun intended).
Whatever the case, it seems a colloquial term which as often is the case, became collectively used for a range of Spanish swords.
I believe we have quite thoroughly digressed from Midelburgo's example.