What I use mostly ressemble to the second collum... I will be back on notation stuff (got to go to work...). They are not junk but exploration... you may never have tried to search for appropriate notation signs to call the other's works junk (even though I really now you tried graphic stuff if I remember well). It's hard to find a correct way to notate microtonality since it's so diverse. That explain the table you gave. Since this one hundred year of research in that field (well... not to talk about temperament of course), composer from different countries produced different signs as you show above.
By the way... my comment above might seem rude, but it's not... don't worry !
I use the IRCAM (research center in Paris) standard notation except for the 3/4tone that I replace with the inverted flat as show at G. So in order from the lowest to the higher alteration in 8th of tones I use in the reference chart above :
G C 'natural' D 2 9 or A 'sharp' B
-1/4 -1/8 0 +1/8 +1/4 +3/8 +1/2 +5/8
You see... in fact there is only two signs to learn for instrumentalists... the 1/4 above and under which are common in contemporary music now. The arrows indicates approximate steps of 1/8th of a tone for these are quiet more difficult to produce and to conceptualize for the musician.
When I had less experience, I use to utilize all these 48 intervals as you might use a 12 tones in dodecaphonic music. But with time, I came up with observation that less than 30 of these are used throughout the major cultures around the world (I name here musical cultures such as occident, asian (indian) and arab music)... I consider that these cultures are the most refined for intervallic organisation. I probably don't need to specify that other cultures got other qualities, of course (to be politically correct).
So now, I tend to use around 27 different intervals in which I found to be the most expressive. -- I'll come back with that later if you wish.