Peter, I have to admit that I am not sure what the
term 'alphasyllabary' originally meant beyond the fact that it
referred to Tamil. I gave up on writing system theory as it was in
1982 since it seemed relatively irrelevant to my purposes. From
then on I have had only idiosyncratic definitions, as you have
rightly observed.
However, I had been thinking that 'alphasyllabary'
and 'neosyllabariy' meant syllabaries that developed from alphabets
or developed after the alphabet; just as logosyllabary was a
syllabary that developed from a logographic system.
Maybe you would tell me how this term has most commonly been
defined. Thank you.