This fascinating scenario brings to mind the Romanitas trilogy by Sophia McDougall, which revolves around a POD of Pertinax discovering Laetus' intended betrayal, thus allowing him to quell the Praetorian revolt that killed him in OTL. Haven't yet decided whether to read the trilogy, but the idea is intriguing.
(Spoiler): The timeline for the trilogy mentions Pertinax's son Publius becoming emperor after his father's death, but there's nothing about Justus, and I can't find anything about a "middle-aged son" in Pertinax's family. Does anyone know if this is an error on McDougall's part, or if Pertinax had another son/heir through adoption, or marriage into his family?
Justus is an invention of mine; I couldn't find any indication of Publius' character or how his father regarded him, so I replaced him with an alternative son who was clearly perceived by his demanding father as 'not up to the job'. The 'middle-aged' bit (in Roman terms), ie around 35-40, is my assumption from the age which Pertinax was by this stage, and a pointer to the fact that the son had reached this age without achieving much or having any useful military record.
The slant of the timeline is to get Pertinax adopting a non-relative as Nerva did, pointing out the parallel between Pertinax and Nerva - Nerva, who replaced an assassinated tyrant killed off by his courtiers, nearly got killed by mutineers in real life 97 and Pertinax did in real life 193 after replacing the similarly killed-off Commodus. (The Praefect who left Pertinax to his fate in reality, Laetus, is butterflied out of the timeline as here Commodus is not emperor so Marcus is appointing less dodgy characters as Praefect than his careless son did.) But Septimius is less careful about his public reputation than the equally brutal (to victims of his army) but more skilful 'master of spin' Trajan was, in both this version and in reality. In reality, it was Caracalla who made the grant of citizenship Empire-wide in 212, not his father; but both men were on the same wavelength in giving top jobs to non-Italians , probably to build up a reliable clientele of provincials who they could trust more. Septimius was also warned to no avail about Caracalla's scheming and homicidal potential; there is a story that Caracalla was suspecting of wanting to stage a coup on the Caledonian campaign once he had shown off his ability and goodwill to the troops but his father ignored it. In real life, once Caracalla was senior emperor to his brother Geta in 211 he invited the latter to a meeting at a 'neutral' venue in their mother's apartments so he did not brign any bodyguards, then stabbed him in front of her.
A more-stable Roman Empire just coming off the apogee of its power and prosperity, avoiding Commodus's reign. They've avoided the further debasing of the currency, though that is still a precedent set by Nero; the utter institutional and bureaucratic chaos caused by Commodus's cronies; the Prætorian Guard being encouraged to act as badly as it pleased, setting in motion the Guard's murder of Pertinax in March 193, the auctioning-off of the Empire, the avarice of the Guard and Didius Julianus; the Year of the Five Emperors Civil War. The younger Severan Emperors will be awarding the Guard higher pay and ever-larger bonuses in their reigns right up to the Barracks Emperors doing it in the Third Century Crisis. It is very likely the corruption of the Guard, the bankrupting of the state by Commodus, and maybe the entire Third Century Crisis has been avoided all together. Though, a quite less severe crisis of succession and civil wars may still happen somewhere in the future of this timeline.
The question is though, when the decline of the Empire really begins. Is it during Septimius Severus's reign or after it?