I don't understand the inner mechanics of TeX, but would this question
be at all similar to the automatic rendering of the custos at the end of
the line? Somehow TeX knows when and where ther line ends, so could a
similar principle be applied to rendering or not rendering a flat based
on whether the line has begun or ended?

Dear Brother,

I'm not forgetting you. In fact the flat feature is even more difficult than the clef duplication avoiding, and requires to completely hack the paragraph builder of TeX. Happily, this will be possible soon in LuaTeX (in fact it's already possible, but too complex). You can have more details on this thread:

http://tug.org/pipermail/luatex/2013-June/004444.html

So I think this will be a Gregorio 2.5 feature... Sorry for the delay!

Thank you,
--
Elie

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