Short answer: We probably will never know the full origins of ancient tuning systems
Who invented or proposed them and how? I couldn't find any resources about those remaining E, A and B ratios.
According to Wikipedia:
Gioseffo Zarlino, in the late sixteenth century, created the first justly intonated 7-tone (diatonic) scale
Whether Zarlino or someone else first created a seven-note diatonic scale, they did not invent the entire JI scale all on their own. Nor does it seem likely that they alone were displeased with Pythagorean tuning and innovated in a vacuum. Ptolemy, for one, is credited in some places with using the 5:4 ratio for thirds.
It's probably not possible to pin down one person or even a sequence of identified tuning innovators through history. The Pythagorean tuning system might have origins before recorded history, and we can't be sure whether or not individual musicians through the millennia were not playing around with different tuning methods.
Tuning with just intonation is based on the overtone series, which is a physical property that any musician with a stringed instrument and enough time on their hands can easily discover on their own. Anyone crafting a wind instrument or playing a "brass" instrument (that is, an instrument of any material where the lips are buzzed into a resonating cylinder or cone) also could discover the overtone series.
In addition, musical instruments and tuning systems underwent parallel development in different parts of the world. There's a tendency to favor the "western" lineage in many academic sources, but tuning systems were definitely developed in Asia and the Americas through antiquity.
Note that Pythagoras did not invent or discover the ratios for the second, fourth, fifth, or octave, either. The fifth (and therefore the fourth also) and octave were known to ancient Mesopotamians and Babylonians and used to tune instruments in those cultures.