THanks for all the suggestions everyone! One thing that I really love about Aikido is that there's not very many definite things. There's so many different ways to do every single technique, and some techniques have very different names according to which "style" of aikido you practice.
Anyways, I asked my sensei last night after class, and his take is for omote and ura (as opposed to the tenkan version) to tenshin with my front foot, and grab under uke's fist and twist kind of like the beginning of shihonage and turn uke out of the way while applying the kotegaeshi grab and then either stepping in front of uke and doing the throw for omote or behind and tenkaning for the ura. It makes sense, kinda. I'll have to practice.
The other amusing bit is that when I looked at the big USAF poster listing the testing requirements, for tsuki kotegaeshi, it justs lists tenkan - not omote and ura. But, since I asked and since sensei spent some time to show me after class, I get the feeling I had better be prepared to do that during the test.
Thanks again everyone! It's really cool to see different takes on how to do this!