This is the requirements in the USAF (this was my exam, though my sensei has slightly modified the test in putting 3 attackers for the randori). It was the exam I was least satisfied with at the time. So good luck.
One thing seems to be clear, across the board everyone is versed in Ushiro Waza by 2nd kyu.
Also everyone so far has HHW which we trade out for KubiNage I suppose.
[We practice HHW but is not required until 1st Kyu...]
I relate to what your last statement said, my 3rd kyu exam was the one I was least satisfied with... hoping to change that for my 2nd kyu.
I just remembered this is even more interesting as some places have 5 kyus and others, like my dojo, have 6. [As of now it appears at around 2nd kyu things are evening out whatever differences may be there initially... as mentioned at least we can do Ushiro Waza together!]