I tune my 12-er down to D about half of the time, and find the need for slightly heavier E and A strings to avoid floppiness. Sounds like you are on the right track. Elixirs are my favorite for twelve's, since I hate to change all those strings.
Another thing I do is switch the wound and octave G strings, so the wound one ends up closer to the ceiling. Since I play finger style much of the time, the up stroke of my index finger always missed the octave G, and something was audibly missing. I simply swapped them, but had to open up the nut slot slightly. There is no downside when strumming.