Rashomon, at the core of the movie, is about the subjective point of view of reality. Four people see the same events transpire. While the events are roughly consistent in the facts of the events, the framing and motivation attached to each of the events differs.
The "play it straight" setup of the characters recounting their experiences is out, the low-bandwith voice and hand-waving in lieu of direct experiences will make it difficult for the characters to frame their stories with any level of different subjectivity. As the players listen to each other's stories, the subjective consensus tends to converge on an accepted reality.
Instead of going pure rashomon, it may be preferable to go with something like Leverage's Rashomon Job. While not quite as "hard hitting" as the original movie, it contains more action and is resolved far more neatly.
What system supports and allows players to highlight characters with different subjective constructions of reality? What instructions and encounter setup will be necessary to provide for the cognitive dissonance that provides enjoyment in the movie?