I feel like I personally can only recall seeing ようにする in some sort of “tried to do” sense so I interpreted it more the way @TobiasW did and yeah, figured that the loop is exhausting so they actively worked to not drive themselves crazy knowing how long it had been. I wouldn’t say with any degree of confidence I’m right over you here though… 
It seems that you are right - and I have confused ～ように with ～のように 
申し訳ございません 
Or maybe not?
In the description on this site, (in the " Compared to 〜のように" paragraph) the の is in parentheses, so maybe it’s optional (especially in spoken language), and actually ように can mean both things? I’m getting more and more confused…
This construction is not to be confused with the use of 〜（の）ように meaning ‘in the way of ~’ or ‘like ~’. Sometimes ように may be followed by a form of する, which can make the two constructions look very similar.
From bunpro on:
Like in this case, の tends to be involved with nouns or noun-like objects. Another phrase of my head would be certain uses of suru verbs, eg. 勉強の仕方. I feel like one of those linguist types is about to lose their stuff and yell at us all, but… yeah, no way I’m remember the proper terms for all of this stuff just yet.
(And Bunpro has a free tier, so this isn’t like super secret paid content or anything)
Yeah, that’s the goal, but the way to forcibly achieve that is repeatedly “have them die” i.e. killing them each loop:
Of course they don’t stay dead, but it seems that’s what he did when Tyler first met him: He killed his beastly fellow loopers for one last time. Next loop, they were in a coma.
Verb + ように + Verb, like @adamstan earlier described, is a pattern that “may be used with almost any noun/verb, to show that they are being done/existing in a particular manner”. So I guess it could be something like “they were acting in a way that was not keeping awareness of the flow of time” after all, maybe.
Ah, I must have overlooked that 死を繰り返し与える part. If that’s the case, you’re right.
This chapter is weird. The story have basically been cut off at the knees. If everything we just learnt about looping is true, then all Hilda and Tyler need to do is not go insane for max 15 years (if they want to experience it all). And Leona will be back to normal and so will the world.
Of course, all of them will be some version of insane or scarred by being stuck like this. 20-30 years?! Really? Like that number is just waaaay too high without all of them going insane. Considering the loopers who stay awake through the whole thing actually remember all that time. No way are they gonna be normally functioning people anymore… Maybe it is better to go into a coma so everything will seem like a dream.
I think the thing that would really kill it for me is that everything returns to the same state, even teleporting our Loopers back to where they were when their looping started… Can’t travel the world. Can you imagine how much easier it would be to visit all the spots in the world you want to see with 20-30 extra years? But alas, not.
Although considering the unlimited money Mia seems to have, maybe there is some way to keep things across loops (same with the badges they all wear). Then some possibilities open up like learning new skills, and such.
Assuming that everything we learnt are true for earlier period loopers, these loopers probably have more problems—or else what will this VN be about? And if we look at the OP video, Leona seems to actually be part of the action, so they will be able to wake her? At least that is my guess. Or the whole story isn’t inside the loops (aka we get out of them at some point and have more story after). 
So technically the only outstanding questions we are left with—aside from why didn’t it end? 
—are what about the fairytale in the prologue and what about 探し女 (and maybe what about Leona awake in the video).
Kinda weird place to be in the story.
Now time for me to go read what everyone else thought…
That is so terrifying. O_O
Very much the same here. I also thought it was a misunderstanding, but nope. And same on having to kill comrades every day.
