Vowels are the easiest bit, to tell the truth; at least, they are from a surface level. Front, central, back; high, mid, low. Easily represented by a series of lines ordered around that structure, with vertical lines representing frontness and horizontal lines representing height, as illustrated below.
(In this case, MS Paint > Photoshop. Ignore the size differences, though; they're a product of laziness.)
Front vowels:
Central vowels:
Back vowels:
With the addition of diacritics to indicate secondary manners. Now, isn't this much less confusing than 'BV' and 'FV' and what if you mean to indicate 'the voiced labiodental fricative' rather than 'any vowel'? And furthermore, it allows you to indicate multiple types of vowels with little effort, simply by putting in all the lines that are pertinent (a maximum of six short strokes, like tian). Very useful for writing up phonemic analyses.
(Of course, it fails at subtle distinctions within the same region, like the two mid-central vowels in English -- but our professor wouldn't have even brought it up if I hadn't specifically asked, so I suppose it's not of great importance.)
Consonants are much more complicated. I thought about using points of articulation as the base symbols -- all dentals based around a simplified shape representing a tooth, for example. But that's so much more subjective and ambiguous -- what looks like a representation of a tooth to me may not seem toothlike to anyone else, whereas front, middle and back can be represented with a minimum of detail.
I don't know. Maybe it's worth devising a system along those lines -- point as base, manner as major modification, secondary manners (in which I include nasality) as diacritics -- regardless of immediate clarity to other people. After all, the whole reason I started thinking about this was because the professor admitted that 'it's complicated [paraquote] when one attempts to notate anything but the most specific or most general phonetic environments.
EDIT:
Tentative point-of-articulation symbols:
It's the typical order. From left to right: labial, labiodental, interdental, dental, alveolar, palatal, velar, glottal.
I don't know if it makes sense to anyone else; it's partly based on the popular vocal tract diagram in that it takes the side view as its reference; e.g., the labial symbol imitates the shape of the lip, the palatal follows the curve of the palate, et cetera.
Under this system, manners of articulation would be indicated by major modifications to the body of the symbol: a vertical line down the middle for plosives (representing the physical blockage), a horizontal line for fricatives (indicating the passage of some air) and circle for resonants (because they're very open). I toyed with the idea of just making resonants unmarked, but unmarked base symbols should ideally indicate 'any consonant at this region'.
As for secondary manners, well, diacritics are a familiar part of these notations. The trick is to standardise them, at least internally, so that a mark does not mean one thing over a certain symbol and a different thing over a different symbol. The exact form of the diacritics is less important and don't warrant illustration.
Yeah, I said I wasn't going to post here. And I made good on my word for how many years? But sometimes one wishes to rant and tangentialise and spontaneously employ British-English spellings in a space away from one's RL everyday acquaintances. Writing on the internet gives one the delightful feeling of shouting at the wind -- someone might hear, or care, or not at all, but it's somehow more satisfying than writing for oneself alone.