Some scattered thoughts from someone who fiddled with Duos for a long time:
270c and 280c displays are exactly the same internally, and I believe that the same display was used in the 180c, though this I have not seen with my own eyes (the 270c and 280c I have). The 270/280c display will also work on a 280 logic board. In such a case, however, you need the whole assembly, as the plastics etc. are different.
The 2300c display actually seems to be based on a different technology, since as well as being physically larger and off-centred, it is recognizable as a "standard" screen of the period, whereas the 270/280c display is very different -- being glassy and less pixellated, almost like a modern MacBook's.
When I do fire it up, whic is not often these days, I like to use my 270c in B&W, as it is gem-like and just beautiful, but because of the size and larger resolution, the 2300c screen is easier on the eye at my age.
Much the same "glassy" effect, btw, is also what you have on a PowerBook 180 in greyscale, and this is why people rave about them. That screen is better than, say, a Compact's CRT.
The 2300c display will not connect to the 270/280c logic board. Been there and tried that; no workie.