Going and rereading the previous chapters, and idea I'm getting is that "sui" might actually be either a
grammatical mood marker? So that "imu sui" would indicate some sort of
realis mood, i.e. either a fact or something you view as a fact. That being derived from "yes" wouldn't be too odd.
"Gosu sui" could then be an
imperative of some sort. In terms of actions, I think that this would fit with your misunderstanding of them as "me" and "you," as when describing things, you're typically more sure about yourself and more "commanding" other people.
Taking into account that the author is Japanese also supports this, I think, because in the Japanese language there's sort of a taboo on directly describing what people besides yourself intend on doing. You have to specify that you
think that they intend on it, instead.
Anyway, the rest of the "...sui" constructions in the manga so far are:
- "Toju sui" in Ch1, when she's afraid of Ryouta after he starts moving towards the sword. So it might be a stronger imperative form? We see the now-definide "oupu" here, (Both with and without "na," so maybe that's a verbalizing particle or something?) so she might be saying something like "stop right now," whereas if she had used "gosu sui" it would be something closer to "please stop."
- Also, in the same panel as the previous, we see a "gosu" + a long construction + "sui." Could be something more like pleading, I guess? "Stop. Please stop" or the like, using both direct and indirect forms. (Could also be elaboration on "why" she's making the request, as I describe a bit more in-depth on point #5.) The whole thing does end in a lengthened "tojuu," though, so maybe the "sui" constructions can appear at the end of sentences, as well?
- At the end of this chapter, then, we see "momu sui na oupu tui ai-." We sort of know what "na oupu" means, so this is probably some sort of request for Ryouta to stay while she collects the writing utensils. It might be a more hesitant request? Or maybe it's an optative? Or it could be something a bit more like "alright, hold on a moment while I..." Basically affirming that she's saying this becauseshe's carrying out his request. "Do this for your own sake" or something.
We see this one again this chapter, followed by "na oupu" on page five right before she tells him she's leaving and asks him to stay put, which definitely seems to support the idea of it marking a command or suggestion of some sort.
- In Ch2, we see "imu sui" for the first time when she's giving her name(?). This seems to support the realis mood theory, as your name is probably the prime example of the sort of fact that you'd want to present as such, considering how most cultures see the name as something that defines a person, and that it's something you can usually be fairly confident in.
- In this chapter, we see a long construction of "go ja tautan tou duu, ni ma ni e ne e a sui." It's a very long construction, similar to the long one in the first "gosu sui" from chapter one. Maybe that's meant to give elaboration on the reason for the command? Like "gosu ~~~~ sui ~~~~" is "Please (because ~~~~) do ~~~~" and "imu ~~~~ sui ~~~~" is "I know (because ~~~~) that ~~~~" or something. Could also mean that I'm wrong about it being a mood marker, though.
- Finally, at the end of this chapter, in the tinted flashback boxes, we see "Oupu jaa sui." This is from her response to him pointing at the pen-brush thing and asking what it is. Considering the use of "oupu" here, I might imagine this to indicate disagreement of some sort? Considering the context here, it's possible that what she said is meant to be something like "I don't understand what you're saying." I've also considered it being a response form of some sort, vaguely similar to Japanese んだ, but less confident on that. Plus, the line that includes it is in a thought bubble, and while it's in his flashback, (suggesting that he might have heard it) it at least implies that it wasn't directed at him in the way a response would probably be.