Ok, just watched the complete rabbit stuff, here are some thoughts:
First a quote I found on the internet:
"In many mythic traditions, rabbits and hares were archetypal symbols of femininity, associated with the lunar cycle, fertility, longevity, and rebirth. But if we dig a little deeper into their stories we find that they are also contradictory, paradoxical creatures: symbols of both cleverness and foolishness, of femininity and androgny, of cowardice and courage, of rampant sexuality and virginal purity. In some lands, Hare is the messenger of the Great Goddess, moving by moonlight between the human world and the realm of the gods."
The solo scenes of Jack and Suzie: both times they say "something's wrong". Both times they mention the smiling teeth.
The solo scenes of all three: The burning match in the background. They start some sort of chant. They disappear in the end.
Smiling teeth: reminds me of Sue's/"phantom reflection Sue"'s face of smiling teeth. Suzie sings: "Dark smiling teeth". The face of your own evil.
The burning match: reminds me of burning the hole in the silk. Does it open up a hole in their "inner cage" in order to realize and overcome their evilness?
The chanting/humming: Jacks "Oh, Oh, something's wrong, oh" which turns into "Ommmm" followed by humming. The chanting of all three characters and especially the "Ommmm" reminds me of chakras as part of transcendental meditation. The whole solo scenes to me have a strong feel of realizing/understanding. Meditating to overcome the inner evil and achieve purity?
I would like to quote from your interpretation: " The funny thing is that the faces are the same, but the roles are very much switched around. It's quite possible, in fact, that we can extend the Lost Girl/Sue reincarnation to some of the other characters—to Smithy and Doris Side at the very least. Yes, I'm suggesting an ensemble reincarnation. It's as if the characters from the massively tragic Old Poland drama are made to experience the same story again, but this time—in Inland Empire—from different points of view."
Audience laughter: when they refer to time. They wonder how far they've come in their process of getting free from this purgatory. This is met by laughter because they still believe they can resolve this by waiting for something outside to remedy their situation. Laughter when Jack asks "did he say anything?" No, dude, you can't "solve" this by having others tell you the "truth". You have to find it inside yourself.
Applause: when they free themselves in the solo scenes by facing (all that talk about darkness, fire, blood, etc...) and overcoming their evilness. Problem with this: I can't quite fit in the massive applause when they enter through the door. Is it for coming back? Doesn't make sense because being in the room means they still fail to reach enlightenment. My guess is the applause is for the things they did outside, playing their part in the ongoing "realization process".
Puzzling this together:
The three characters/rabbits all reincarnate. But with switched roles. Why? To get enlightenment by experiencing the "drama" from another perspective. As you wrote in part 3: "There would be obvious spiritual reasons for this — expansion of experience, development of empathy, perfection of the soul, and good-old-fashioned karma."
When the three rabbits are in the room together, waiting to go for "another round" they try to understand but fail. They still keep their secrets ("Noone can know"), they are still trapped in their incomplete state of mind.
In the solo scenes, they begin to understand. When they reach enlightenment, they simply fade from the waiting room/purgatory. They don't go out the door, because that's not the escape route. It's the inner reflection and understanding that frees them.