Since it is two diffrent parts of the song, could you use 2 diffrent sounding guitars? One accoustic and one electric, or one muddy and one clean? Maybe that is a way to play both chords at the same time.

Have you tried Major sevenths and minor sevenths?

What about having the guitar go silent for 2 beats? (You did say it was half a measure.)

Maybe you could go to the piano and try playing the chord you hear in your head. If you can do that then start trying to remove notes and see which notes are the ones you have to have to produce the sound you are hearing in your head. Maybe you can get it down to needing only 4 or 5 or 6 notes to make the elusive sound you seek. After all A and E chords share the E note already.