...As regards Beyond, it should be noted that we never really heard of a separate "cargo transporter" or "cargo transporting setting" that would not have been compatible with people. TOS and TNG both show transporters beaming up people unawares; we see a stowaway beam up onto a special platform that was intended to beam up cargo only, and was never seen beaming up people ("Dagger of the Mind"), or a transporter specifically intended for moving cargo nevertheless moving people ("The Hunted", say).
Would the Franklin platform really be in need of modifying in order to be people-compatible? In "Broken Bow", it sounded as if Starfleet man-rated the transporter just by stating "We now believe it's fine for Ensigns just as well as for fruit and stembolts", rather than actually changing anything about the mechanism. Quite possibly, a transporter is a transporter is a transporter, and if it works at all, it works on every possible transportee.
(Now, when DS9 introduces Kasidy Yates, it also introduces different Marks of transporter, some of which cope better with difficult materials. But even all the previous Marks obviously coped with people, from "Broken Bow" on; we have no real evidence that machines from before "Broken Bow" would have been unable to cope with people, even if they couldn't handle handwavium powder or unobtainium bullion.)
Obviously, Scotty would gulp a couple of times when applying a device whose makers never actually thought in terms of man-rating it, but he need not have done anything beyond that gulping, and indeed might not have been able to do anything beyond that.
It's just that it's also possible to believe the opposite, that the different Marks actually behave sufficiently differently that some of them (chiefly the early human models) are a hazard to life and limb. The premise of "Daedalus" is close to that, and "Realm of Fear" also hints at progress being made on safety, although this could have been progress from the original and inherent 99.9999% to 99.99999% safety and in practice has only a psychological effect on the users. Perhaps, just perhaps, the machines moved over the "truly safe for people" hurdle at two different times in two different timelines (even though we really have every reason to believe this happened in the 2150s already at the very latest, rather than after 2233)?
Of course, Scotty never was much of a transporter specialist in TOS: it was Spock's cross-circuiting to B that saved lives there. Our alternate Scotty here might simply be our replacement McCoy: the man with so much knowledge that he actually starts to worry, even when the technology is exactly that of the Prime timeline where his layman Doppelgänger was content to just slide the sliders.
Timo Saloniemi