#achronicity

We already know that not only hostless monsters are hard to kill, but that it transfers to the infected host over time. This would mean that they either already existed beforehand and just were experimented on or discovered durning the search to improve humans. To elaborate:

If they were a thing, all of this would be common knowledge, since a group can keep things under wraps  only for so long. After all, they are somewhat parasitic, thus they would be around for long enough that some secret society would sooner or later make a major blunder. Thus, the crew would likely remember a thing or two about them (defying that would involve much more throughout memory tampering).

If we roll with the idea that this mess has a starting point, we can easly assume that it was caused by Achronists doing something for SCIENCE! For instance, the moment they opened the Doors something could have gotten to Earth from off-world. The other reason why peeking through them might have been the cause could be that it yelded results. Technology that isn't quite on the same level as the rest of the world or unknown metals. The organisation could even be fed juicy information that ended up doing more harm than good.

Given that the initial intention was probably to use what they found for their cause, this lets us suspect that the monsters were used either as vectors to fuse alien technology with humans or the solution itself. But noone in their right mind would want to wear a permament mask and be inky in one way or another. Unless the situation became particularly dire. Which was probably caused by the very same event that made monstrosity come into play. Even through monsters cannot leave the Facility of Nothing, it's possible that the situation calls for more long-lived, mentally coherent people which is one of the possible reasons why Cancel is doing this. Or that the less coherent inhabitants of the place are kept in check by unspecified limiters.

Why would the overarching plan be so important? Because there still might be people in stasis waiting for better times. That would put them in a position of relative safety.

Moreover, this can also limit the possibilities of why this is the last iteration - some people might be more attuned to the whole mask business. For instance, the participants of the Human Game could be singled out of those who were close enough to the ground zero at some point.

If one thinks about it, this could also explain why masks can start showing expressions after a while - their looks would be so far off typical humans that it would fool exactly nobody and it seems like a grand waste of resources that could be spent towards PURE MURDER... unless the plan is to interact with sapient species. Then the quirk would have actual purpose.

This is a reasonable assumption if one were to skim transcripts of what could possibly be early snags in the plan. There are two plot-relevant things that could be this mad - monsters in general and the Beast.

We don't know much about the Beast, but if it were both a "fruit of desperation" and a control sample of sorts, this could mean that the Beast was the first person that undertook the early masking attempts and were successful... to a limited extent. It rages like the others, but might have goals beyond "kill everything to death forever". Thus, if the host could keep their wits about them, the end result would be a nigh-immortal specimen able to carry out long-term plans.

As to their small-scale beginnings...

Monsters weren't created (implictly - by an outside, premediated influrence), but they can breed. Since they are exothermic, this means they have an internal supply of power. If it were limited, this would explain both the parasitism (the search of a source of energy), and that the first changes to the host are geared towards making them inseparable - after all, expanding energy to infect and then having to find another host would be incredibly risky.

The other reason could be that they are geared from the start to infect very specific humans. This has plenty of implications:

In this case, the metallic masks would be there from the beginning and not formed ad hoc as a host is found. This would enable grouping them in accordance to their shapes. We could even assume that the participants' are sorted into categories depending on how their monsters look like. That in turn could place the forming of the mask in time periods which were erased from their memories. Continuing this chain of logic, next the implication would be that the breeding period might differ from monster to monster (depending on their intended hosts).

This might be the reason why a monster would keep using "we" while doing the verbal meat grinder routine. In the breeding process, a part of the host's body might be used (if not the whole host) - if only to give a marker for who to look for, how to lure them and how to break them. Some unspecified thing that would act as a temporary supply of energy to move could also be a reason.

Since killing a hostless monster leads to Bad Things, they might have something that is in some way important to the desired hosts.

Of course, this still leaves us with "who made it possible if Achronists weren't responsible for the research on monsters".

The research could be cheekly be filed under some other term.

What was left of Achronists after they opened the Doors might have not called themselves that anymore.

Depending how both of the phrasings are understood, we could read it as "there was no research in the last decade". Since the game itself is at least 40 years old, this doesn't really matter.