Assuming the problem is related to the resolution that the UI is created at... there are no custom UIs made for a vertical height of only 540 pixels, so you would have to make one yourself to really test that out.
My hunch is it has less to do with the UI and is something more fundamental in the game itself. 540 pixels high is basically nil. I'm not sure EQ2 would work in the archaic resolution of 800x600 (which is about as low as I think most things would ever go these days). You could try setting your resolution to that and seeing if the game will run at all; if it doesn't, then there's most likely no way for you to run 4 screens on a 1920x1080 resolution.
I normally play at that resolution, and a quick test of minimizing shows that the minimum resolution it would go to is around 2/3 of the vertical height. Looking in the way-old EQ2 game configuration program, the minimum resolution it lists is 1024x768, which fits that ~2/3 height. There simply may be no way around that minimum. In that case, your only hope for 4 copies on 1 screen would be to have to overlap them or to go to a higher-resolution computer screen.
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