For me, as long I can be made to believe that it is a form of telepathic communication, separate and distinct from spoken communication, that would be sufficient. It really wouldn't matter too much how "realistic" it is beyond a certain point, since that's not what makes a good movie, TV show or play in my opinion. If there were going to be a live-action or animated adaptation of Outsider, I'd prefer they spent the budget on the best writers and actors possible to immerse me in the story and make me believe I'm experiencing it firsthand. (And gimme an epic soundtrack, too.)
That being said, here is how I might go about portraying sanzai in a creative fashion, if the story were told either from an omniscient or third-person POV that necessitated the audience being privy to the interaction:
The Insider page on Loroi telepathy has this to say about it:
The content of the message is not exactly transmission of “thought” or “emotion,” but is faster and more expressive than spoken language. The amount of information carried per second via sending is about five times the information carried in normal speech, but since a lot of the bandwidth is used to add nuance and deeper meaning to the message, sending operates at only about twice the speed of speech. Think of it as if sending was a spoken message with subtitles, a music track and mood lighting.
To start with, the well-established technique of a voiceover with some distortion would be sufficient to carry the spoken message and the perhaps ethereal quality of experiencing a "voice" inside your head. And, of course, facial expressions and body language would be important as well, as we do see Loroi using these the same way humans do, even when sending. They laugh and smile, and they frown and scowl. We already understand this language, so it's easy to portray. Since much of the rest of the information conveyed in the message is for nuance and context, there are a few methods available to add this kind of subtext.
One way is with lighting and color. This, too, is a pretty well-established and highly versatile technique in cinematography. Let's suppose Beryl is sending a lighthearted, friendly greeting to one of her companions (<<Good morning, Fireblade!>>). Casting a somewhat brighter light on her face than the ambient light, allowing the viewer to see all of her facial features in sharper focus and contrast, and perhaps creating a "glow" of warmer lighting around her would serve to enhance the friendliness and openness of her message. On the other hand, let's have Fireblade responding rather icily to Beryl's greeting, for whatever reason (<<Go away. Leave me alone.>>). We can dim the lighting around Fireblade to make it seem like there's a figurative dark cloud hanging over her. We can move the lights around to a different angle to cast shadows across her face in a way that expresses her aloofness and desire to be left alone. Being able to seamlessly transition lighting and coloring styles not only between characters but for the same character as her mood changes would help to make it seem like a natural part of her being and her way of communicating.
The use of music and sound is another method for adding or enhancing the mood or feel of a sequence that most film-makers already use quite adeptly. This might be harder to work into brief sanzai conversations, but a longer one where there is a definite or dominant overall mood to the interaction is where any reasonably talented composer can write music to underscore that mood. There could also be a motif or series of motifs associated with each character; a way to identify them by ear, and also to emphasize the fact that each Loroi has her own, unique telepathic "signature." Or it could be something as simple as a few subtly-changing notes on a single instrument or synthesizer that may crescendo and decrescendo to "weave" it in and out of the dialogue.
There's a final touch that I might consider adding which, I think, if done right and used sparingly, could add a really interesting and unique element. We've seen in the comic that characters with telekinetic abilities are shown to have glowing eyes when using those abilities. I might use a similar effect when a Loroi is feeling a particularly intense emotion or in an otherwise rare state of mind. As an example, in the anime Rurouni Kenshin, the titular character's eyes change color from their regular violet or purple to gold in very rare instances (I think it only happens four times in the entire series) when he reverts to his former personality as an assassin. On those occasions, he is possessed of a strong intent to kill someone. With CGI or very creative application of lighting or filters, it should be possible to make a Loroi's eyes literally "flash" in extreme anger or rage, take on a hollow or deadened look in hopelessness or despair, or brighten in moments of happiness and joy -- beyond what an actress could accomplish with her own talent for portraying human characters.
Any or all of these, if used right (i.e., subtly enough that one might not even notice it the first time you watched it), could help to set sanzai apart from your basic portrayal of telepathy as a disembodied voice without being too distracting for the viewer.