Careful what you wish for
This first one is a very minor nitpick. The administrative "diocese" were part of the political reforms of Diocletianus, and before his reign, the province was still the basic unit of imperial administration with each province being wholly autonomous and only subject to the emperor (which was a big causal factor in the actual crisis). A more appropriate name would simply by "Syria", which roughly corresponds to the Diocese of the Oriens which was later established.
Yeah, I later found that out, but I was afraid to repeat the word "Syria" too much.
Also minor, but this picture appears to be of the Milvian Bridge. Normally I wouldn't nitpick something like that since I use images depicting IOTL events to portray ATL events all the time, but it is very significant in this picture because the soldier's shields prominently feature the Chi Rho, which Constantine allegedly saw in a dream prophesying his victory against Maxentius. Not sure if anyone else minds; that's just something that stuck out to me.
I found this picture by looking up the words "Late Roman Army" on Google. It was made by a deviantart user, and I found it pretty cool. I can change it if it's too jarring for you.
On some level, a parallel of the events of OTL's crisis makes sense. After all, imperial usurpers were typically powerful, wealthy men, and this isn't likely to change drastically this quickly after the POD. However, I feel compelled to point out that the rise of several of these men was highly contingent on previous events. For example, Aemilianus was a prominent general in Moesia after the disastrous Battle of Abrittus, and the lackluster response of the reigning emperor Gallus instigated the Moesian army to declare Aemilianus emperor. Without Decius dying at Abrittus and the Gothic host being accommodated by Gallus thereafter, I have my doubts as to whether Aemilianus would have the opportunity to become emperor. The same can be said of Gallienus. Without his father's fortuitous control of the Rhine legions at the time of Aemilianus' usurpation, I have my doubts as to whether or not he would be enough of a political force on his own to become emperor. That's just my opinion though, take it or leave it.
I confess that my knowledge of this area is quite lacking, but as you said, many of these men were wealthy and powerful in their own right, and they would have a chance to take power and hold it for at least a few months. However, if you have any suggestions, I can edit the bits in question. It's not like any of the men cited there (other than Gallienus) will play a big role in the story.
Maybe you explained this and I missed it, but I have my doubts as to whether or not any Gothic state would be equipped with the institutions or resources to permanently occupy the Roman empire at this time. Even after Adrianople a century and a half later, the Goths were not able to establish such a state and it would be another few decades before Alaric could leverage that sort of concession. So how exactly were the Goths able to do this so early ITTL?
This "Gothic Kingdom" is less an organized state and more a tenuous confederation (united under a charismatic king) that is currently occupying a bunch of territory with a few cities. It'll take some time to consolidate -- if it is given that chance. It'll fall apart the moment Rome gets its stuff together -- if it manages to survive the apocalyptic situation it is in. The Goths are also lucky enough that Odaenathus is currently too busy consolidating his kingdom and interfering in Iranian politics to attack them.