I was thinking of getting the Ostrogoths to Asia Minor more as part of a relocation attempt gone horribly wrong rather than a hostile takeover.
You'd notice, however, that few important foederati ever remained at the place that they were assigned. Sooner or later, and rather sooner, it would end with a conflict.
Now, not only it would be outright suicide to relocate foederati or laeti down to your untouched provinces but it would be a bit weird when clearly you need them at the hot borders: a foedus is about supplying a region that needs manpower for production and military support.
And if there's a region where that's not prioritary at this point, it's Oriens, and one that needs it are the Danubian provinces.
Only once they're across do they take over the region and build their own navy that allows them to contest the Aegean and western Greece.
Which again, implies the Empire being unable to stop them building a navy, a situation that existed IOTL and lead to the Vandalic raids in Italy. Only, this time, ERE is obviously unable to supply naval forces for the west. It's basically the worst-case scenario for Late Romania : loosing the naval edge on both sides of the Mediterranean, allowing Barbarians to take whatever please them or at the very best being dependent on their alliance (which often backfired).
From everything I've read, in its early years, the population of Constantinople was largely Latin-speaking (unlike most of the other important cities all around it).
Problem is that early years of the city saw a really limited population (on which "largely" Latin is a bit exaggerated, considering population from Anatolia was settled there) to begin with, with very serious talks about abandoning the place after Constantin's death. The city really grew up, specifically demographically, not before a relatively long period.
Likewise, the Balkan hinterland was also in the latin sphere.
I disagree on several points there : the Jireček line roughly cut the peninsula in two halves, and the southern one was by far the most important demographically, with the northern one being not only more sparesely populated but with important non-romance populations.
If the constant war with the Ostrogoths leads to the same level of devastation in the Marmara Sea and western Asia Minor regions, whilst Moesia stays mostly untouched, I don't see why the opposite result wrt Constantinople (i.e. Latin reaches a tipping point instead of Greek) can't happen ITTL.
That doesn't appears really possible : even assuming that you used Ostrogoths for Greuthungi on this map (while they're not the same thing, long story short the ethnogenesis of Ostrogothi can be traced from the collapse of Hunnic hegemony), you didn't get rid of the shitload of other peoples and entities along the Danube : other Gothic entities, what remain of Dacians, Alans, Huns, etc.
Not only the region was weakened by regular raiding since the IIIrd century, but you already have other foederati and laeti present in the region before Greuthingi entered in Romania : Trevingi, Carpi, etc.