That's what I interpret Aced as by now as well, the totally unrepentent and assholish Aced we see in the last few updates of browser-chi (which are not addressed in Back Cover at all) is probably a consequence of him giving up all hope on solving this in a less aggressive and ruthless manner.
Back Cover certainly shows us that he tried to find a less forceful solution first.
Ah yes, I also found that Gula's reasonings for doing it were a little thin as well. Nevertheless, Gula is described as the lone-wolf type who isn't really interested much in overly playing nice and indulging in camaraderie.
It's also telling that at that point Aced is specifically not blaming Gula but Invi as his reactions show, he's more dissappointed and him grabbing Gula by the collar is more out of frustration of what he deems the right way being undone rather than any malice towards the Leopard.
Aced genuinely wanted to work together with Gula both in defending against the Darkness and finding the traitor, since he didn't believe the traitor is actually one of their group of five.
It was not until he learned that Gula not only has the Lost page but also kept it hidden from all of them that he changed stance and considering the circumstances I do think that Aced feeling betrayed is partially justified.
The MoM is really an enigma so far, and I can't yet tell if he's really a malevolent force setting this all up or a neutral/good force playing a bigger long time game that may somehow make the tragedies of the chi-era "neccessary".
The way he sets his pupils up and divides their tasks is highly suspicious though and makes it look like a deliberate setup. Considering how the Master reacts to Gula immediately figuring out his intentions (or what he may want Gula to believe are his intentions) I'm inclined to believe that while Gula is a little withdrawn and likes to keep to himself, he may be the smartest of the five Foretellers and the quickest on the uptake, hence why he got this task out of all. If one is already somewhat shy and likes to keep to him/herself, it is easy to convince such a person to totally withdraw and trust only him/herself when given the proper incentive, which in this case was the grave implication of there being a traitor. It's easy psychology.
However, as Gula himself admits later in the movie (when shit has already hit the fan though) he was a fool to blindly follow the passages of the Lost page, also given that they're according to him ambigiously written in the first place.
I dunno how it was in the original browser-chi, but I faintly recall that it might have been a Chirithy that first mentions a traitor in the game itself.
Ira IS the one to make the fact of a traitor public in the movie and the meeting of the Foretellers is really well done in this regard. Ira deduces that there is a traitor from the fact that he found a Dark Chirithy roaming around, which is undeniable proof that someone succumbed to Darkness and betrayed the light.
As seen the other Foretellers, even Gula, react with shock to the discovery that this is a nightmare.
The Foretellers can summon the Chirithys of all the wielders of their unions (as the Chirithys are also stated to be the link between the wielders and their Foretellers) and as such, as both Invi and Ava correctly point out it is impossible to identify the traitor by summoning their spirits alone as if one of them IS a traitor he/she could just summon an untainted Chirithy from one of their union wielders.
Ava correctly follows that in this case, it cannot be confirmed that the Nightmare has to belong to one of the five Foretellers, as the Nightmare Chirithy could belong to any of the regular wielders in any union.
Ira however counters with the issue of the strength bangle and states his belief (belief, mind you, he has no proof) that it was distributed by the Nightmare and that it is misused against its original design. Just collecting the dark energy and thus purifying things was agreed by all Foretellers to be okay, but using the power collected within it is not, to which Gula adds that it is brilliant move because all spirits look the same and there are countless wielders, it is thus impossible to tell to who this Nightmare belongs to.
On Aced's inquiry on what to do, Ira declares that those strength bangles apparently can't be acquired by just anyone, so he suspects that one of the five is involved.
Note how everything Ira brings forth are just assumptions and conjecture, he doesn't have any reliable proof and Invi calls him out on exactly that.
Aced then understandably chews him out for making such a foolish move and plant first seeds of doubt.
Due to it being his mission Gula certainly knew there would be a traitor beforehand, but even he seemed taken aback that Ira implied it to be one of them, yet started to take that into consideration as well, hence renewing his "trust no one but myself"-mantra.
The Foretellers being so utterly dependent on the Master bothers me a lot as well. They're all so unflexible and basically "helpless" because of it, Aced at least tries to break out of it somewhat and while Ava states her belief that one should act and think for themselves when meeting Ephemer, she herself doesn't act on this realization.
Gula too, he admits that he was foolish just following the Lost page and that it is written so ambigiously that he didn't really made any progress on finding the traitor, yet the solution he comes up with is to "get the Master back to ask him" and worse, plans to do so by summoning Kingdom Hearts, something that isn't even sure to lead to the desired outcome, as Ava rightly points out.
Ira is definitely smart and also serious/composed most of the time, but he also seems to have what I call a tunnel view or "mindcuffs on" and is prone to overthinking things and jumping to conclusions, which shows in how he deals with both Aced during the first half of the movie and with Gula during the latter half.
As for him being "scary" and ruthless, I do believe that in her by now sort of paranoia and fearing for Gula's safety (after all, Aced nearly gutted him and the Leopard was still wounded at the time) Ava misinterpreted Ira's intentions. His "scary" face and such was because he was angry at her for impeding his attempts to make more sense of things.
In the scene beforehand Ira does state to Aced that he would like to believe that Gula is really just carrying out his mission, as it's Aced now who casts doubts on Gula's true intentions, and that he wants to settle the matter himself. He then walks away and states "I need to see that Lost Page".
Thus, Ira wants to get Gula in order to demand seeing the Lost Page, not to actually "end" him.
As for Invi, she certainly genuinely tried but she also only did half of her assigned task as her keeping the group together and being a mediator took a backseat to the observing role and reporting to Ira. Her trying to distance herself from Ira was a nice gesture, but a) she only said her reports would become "less frequent" not that she'll stop completely, b) none of the other Foretellers actually knew about this gesture of her and c) as Aced correctly pointed out she should never have done that in the first place to begin with, the damage and distrust was already there. Not to mention that Invi didn't stop as Ava later on the scene on the bridge confronts her about telling Ira that both she and Gula are in hiding.
Gula letting out that it was Invi bringing him to cancel the alliance was just the drop that made the glass overflow as in Aced's eyes it confirmed what he already had suspected. Note that he isn't really angry or anything at Gula himself, him getting physical there is just frustration, but is seething with rage at Invi for "always getting in the way" as he later openly accuses her.
Of course Invi IS correct of not amassing too much power, but the way she went about it only served to indeed make things worse.
Oh yea, Gula assuming Aced might be the traitor was definitely part of the "false leads" he followed which cost him too much time and his efforts to expose him also made things worse, just like Ira's jumping to conclusions, Aced's forceful decisions and demands to outright defy all the Master's teachings, Ava's indecisiveness and passiveness as well as Invi's decision to expand the extent of one part of her role and neglect the other did as well.
In the end, all five of the Foretellers made decisions and took actions that worsened things until they cumulated into into an unresolvable mess.
As for what their actual relationships are by the end, I'm inclined to follow your assessment although I think how Aced and Ira view Ava is subject to debate.