[TL;DR - A theme of the movie: 'There are only two, the third does not belong and must be purged so the two can become one.' Look for the numbers 2 and 3, sets of pairs vs. trios/love-triangles, two girl rabbits and one boy, two fertile and one barren/sterile, Nikki being exposed as a fantasy to help Sue and lost-girl find each other, etc]
Jeremy, if you don't mind my asking, what is the image in your profile pic from? It kind of reminds me of the shape of the red lamp in IE, which also sparked my interest, as it seems to symbolize a trinity of some sort, which struck me because initially I was only thinking of the pairs of characters, when actually there are many more instances of characters/entities in groups of three. Maybe the Phantom represents the third part of Lynch's holy trinity here? I.e., the three main characters of everyone's life are themselves, their soul mate, and their spirit guide (could this also be the Phantom maybe? It seems like a stretch but I feel like the 'pairs of two within sets of three' is a common theme, I will give some examples below that may intrigue you)
My first naive and myopic interpretation of the movie was that all of the female characters were representative of mother nature, and all male characters represented mankind. This is especially represented in the first scene with the prostitute lost-girl, which set the whole tone of the movie for me. There is definitely a 'men making women's lives hell' feel to everything that happens, and that to me screamed symbolism of mankind ruining mother nature, but I care about the environment so that is likely me projecting. (funny word that, its two main meanings are a big part of IE)
If you watch the movie with this dualism in mind though, I think you might find some very interesting new ideas, for me what came to light was the concept of two vs. three, e.g., character + lookalike/reincarnation + the Phantom, the two lovers in the multiple love triangles, two of the three in the love triangles being fertile while the 3rd is barren/sterile, the two female rabbits vs the one male rabbit, sue and lost-girl vs. nikki, the two candles lit by one of the two female rabbits while the 3rd male rabbit is absent, the list goes on. There are also multiple instances of grouping 2 females with one male, an obscure example are the homeless people there for sue's death. The 3 rabbits representing Lynch's trinity godhead definitely makes sense, especially if there really is a Polish fable about that. (I plan on searching for that fable and finding out myself)
This is a bit of a silly interpretation, and a small one at that, but I think you'll find the numbers 2 and 3 permeating the entire movie, and the 3rd is almost always hidden/offscreen/ambiguous. I see a few examples of triumph or defeat of 2 due to actions/encouragement/reflection of a 3rd. Also, the male rabbit asks, "Where was I?" in the rabbit scene that happens after the two-candle rabbit scene where he is missing, but fades in and out briefly, the same way the Phantom disappears in Sue's story to Mr. K. I honestly feel like there's an argument to be made for this dynamic pervading the film: one + one's other half +(vs.) fear/evil/negativity. What is striking to me is that there is always one of the three missing, it's not always the phantom, either...as far as I can tell there are no scenes that include sue, lost-girl AND the phantom together. I feel like the two-lights theme is related to this. (Two candles at the seance, two lights reflected on the TV, and two candles lit by the rabbit)
It seems to me that all of this points to, 'There are only two, the third does not belong and must be purged so the two can become one.' This pertains to quite a few dynamics, just think of what a love-triangle murder actually is. Like I said, a bit silly but it's definitely there.
Such a fantastic movie, and I have to say the OP's interpretation seems to be the closest to what Lynch's internal narrative actually was, it really opened my eyes to what was really going on. I was actually a little disappointed in myself for not giving it another watch before looking up online interpretations, but my own was so fantastical I knew it was more myself projecting my own demons onto the screen. Lynch has a way of creating a box we all fill with our own insecurities, hopes, dreams, and fears.
Cheers! Sorry for the long-winded post!