The Dinnerbone or Grum names (I think Grum is correct. Haven't used it in a long time and I usually use Dinnerbone) are not supported by Armor Stands as I'm aware.
Although the Dinnerbone tag won't work, there is another solution, although it may not be what you're looking for. One thing you could try is setting all of the position NBT to 90 (Don't know the NBT tags right now, I'd have to pull them up).
Personally I wouldn't go this route, but here is a better route. Your best bet would be 4 invisible armor stands with armor in each slot (Helmet for Armor Stand 1, Chestplate for Armor Stand 2, etc) and then positioning them based on which armor piece they are equipped with. This could be tedious but for what you're looking for this would be optimal.