I have always tried to view the terms in terms of movement patterns.
Movement locations: omote to the front; ura to the rear.
Movement patterns: irimi-entering; tenkan-turning. Tenkai-pivoting. Soto-turning to the outside. Uchi-turning inside.
Early text by Tohei used the terms irimi and tenkan. This was later revised to omote and ura by hombu from what I can tell. Some of the senseis who went with Tohei used irimi and tenkan and then when they came back to hombu they started to modify the terms (I believe AAA did this from what I have seen of early test requirement terms).