I leave nitpicking over the exact meaning of the words jiyu oyogi and henka waza at the hands of other people.
The understanding I, as non-japanese, have of both concepts within Aikido was taught to me by my teacher and further developed in the talks with 4 pupils of o'sensei.
Having had the advantage both attending several seminars by Tamuara Shihan and speaking with Tamura Shihan peronally I might be able to shed some light on the confusion Aarjan experiences over the concepts.
Two things are very important to realize:
1)Tamura Shihan does not do any Kihon Waza in his seminars. He sometimes names the technique and for emphasising that this is not Kihon Waza he sometimes adds that this is oyo waza, meaning that the "form" he showed and people are invited to find and practice is oyo waza. In other occasions Tamura Shihan showed some Henka waza, but only named the last technique. I guess he expected everybody to know, have noticed and been aware of the beginning technique anyway.
2) Tamura Shihan gives his seminars in French. This means that the explanations by Tamura Shihan are translated into Dutch (in the Netherlands). The quality of the translation depends not only on the language skills of the translator but also on the understanding of the subject itself. Although I must say that the usual translator (Tessa Brouwer) does a fairly decent job at this, it is especially at these more difficult concepts that are not part of the common knowledge at a lot of the aikidoclubs in the Netherlands that I cannot escape the feeling that the translation provided in meaning and value differs from the original explanation Tamura Shihan gave.
At a party after a seminar in Compeigne (in France) I had the opportunity to speak with Tamura Shihan about the normal progress and development within Aikido. As I understood it he explained to me that in Aikido one starts with training Kihon Waza Kihon Gi to built a strong foundation and to study all the details of every technique. From this foundation the student is to develop to a personal creative adaptation. This is what he referd to as jiyu oyogi. He explained that one of the goals is to reach a personal adaptive and creative form which enbodies the idea of takemusu aiki.
As a last note: I have been told by Henry Kono sensei and Alan Ruddock sensei that o'sensei did not actually teach in the way as people think of teaching aikido nowerdays. The development into a "teaching system" was due to the work of his son and the first generation students that went into the world to spread aikido. With that respect we are in my personal view often creating unnecessary problems, or at least problems that in o'sensei's time simply didnot exist.