Let’s not forget that the emperor spent years physically battling hordes of demons and then went straight into a 1v5 with four chaos and his son and won. Horus fought an angel prior, while the emperor spent years waging war against all of hell and went straight into that battle without respite.

About 15:00. You're right, swordsmanship doesn't work. Good addition here would be the primarchs are great swordsman and while the emporer is as well, hes also rather partial to the ak47 strapped to his hip. Or maybe more accurately cruise missile or maybe atom bomb...

Many say Monarchia was a massive mistake by the Emperor, but I see the reasoning.
It's a perfect demonstration of what submission to a true deity would be like. No respect, no choice, and no recourse is possible. You have no rights, no voice to disagree, no ability to resist or abstain.
That's what serving a god is like, and Lorgar and his legion utterly hated the taste they got on Monarchia.

It turned out badly, but I think the Emperor demonstrated his actual argument very well there: "You wouldn't like me as a god."

The Alpha legion didn't actually turn completely traitor. They intentionally spit their legion to prevent either side from decisively winning the civil war. The goal was to prevent humanities extinction by preventing either of the two futures they knew would cause it. If the four best guys opposed the emperor, I don't think chaos is likely involved on their team unless you change their stories and characters radically. The reason they might unite against the emperor would be if they believed he was about to do something that would render humanity extinct. If that were the case the alpha legion might completely support them if their story remains the same and they haven't somehow been corrupted. If the alpha legion were corrupted they might be the cause of the entire civil war. The "loyalist" side might actually have been  infiltrated by chaos seeking to weaken and undermine the imperium. The alpha legion could force Magnus to break into the webway by sabotaging any other means of communicating with the emperor. Then orchestrate demonic possessions and chaos corruption to make it look like loyalist forces are completely run by the ruinous powers. The ultimate goal being the death of the Emperor which in this scenario might have been an overwhelming defeat if the alpha legions treachery isn't exposed soon enough. If it is exposed then when and by who would greatly influence the outcome. Alternate histories are tricky though, most of the primarchs have a backup in case they failed. Likely since they were designed to with a couple of exceptions.  Guilliman, Magnus, maybe Vulcan, and maybe the Alpharius twins. There are two missing primarchs who might have served two those roles and it isn't really clear if there was actually meant to be Alpharius twins. For that matter there might not have ever been twins, but that is a whole other rabbit hole. The point is I think big E expected half to get messed up and for the other half to be what's necessary to win the inevitable civil war. To make an alternate heresy you tend to need to mess up your  traitor faction and prop up the loyalist faction. In both actions you radically change the characters and make it harder to predict unless you work backwards from big E ending up in the chair. Only one I could think of that doesn't is an Alpharius heresy, but that as stated earlier, has other complications. Fun stuff to consider though.