If we did them as
ornaments the possibility would arise of being able to use them to set
English Virginal Music which uses the slash and double slash,
those behave rather differently from ornaments, being as you say,
through the stem.
through the stem, extensively - although as folks have noted, nobody
really knows what they mean.
You may like to look at Denemo's output, as it has a claveciniste menu
for French ornaments - it also generates coulés which, again, do not
have the normal attributes of ornaments, so you could get an idea of the
syntax needed for those too.