Tenchi Muyou! Ryououki: Heianmuyo! Picture Drama

Caveat: my Japanese is extremely limited (aside from anime, I spent four years in Japan, but that was a decade and a half ago), so the lack of English subtitles (in the version that I was able to find) hampered my ability to understand the events and enjoy the show fully.

It's not (at the time of this writing) easily found or widely available through online streaming sites, but is probably worth the time and effort to search it out _after_ having watched at least one season of Tenchi Muyo Ryooki, or one of the other main series (possibly excepting Mahou Shoujo Pretty Sammy or Dual ... Parallel -- not as a reflection on them, but because the other Tenchi series seem more in line with the Heianmuyo characterization, and having first become emotionally invested in those characters would likely give the viewer a better feel of those found in this picture drama).

It's a picture drama (basically just has audio accompanied by still images, though there is some very limited animation such as camera pans and zooms and a "page turning" animation between different images) where it seems Aeka imagines various Tenchi Muyou! characters in a story set in the Heian era of Japan. Irrelevant as far as I can tell to the main plot of the Tenchi Muyou! Ryououki OVAs, but completionists can feel free to watch it. It references a few stories and elements of Japanese folklore.

In the end it finishes inconclusively as Aeka says she can't take any more of this world.