Basically, this is what I see happening:
This assumes that the Federated Commonwealth did NOT fall back when the Combine counter assaulted them in the War of 3039. One change, that snowballs into others.
The Federated Commonwealth armies continue moving forward, crushing the Combine forces and turning it into a protectorate of the Federated Commonwealth. The Coordinator is forced to support Hanse' claim to the First Lord position in exchange for limited self rule authority. Rasalhague (surrounded) and St. Ives place their official support behind him as well.
The Free Worlds League, still recovering from absorbing Andurien, and the Capellans, still recovering from the Andurien/Canopian invasion, do not have the power to resist Hanse Davion. Chancellor Romano Liao dies in a palace coup and Tormano Liao is welcomed as the new Chancellor. He agrees to support Hanse's claim. Surrounded, Thomas Marik follows their example, as does ComStar, and the Star League is officially reformed.
It's official capital is Terra, but Hanse rarely goes there and the defacto capital is New Avalon.
3041: Clans learn of the reformed Star League and instantly vote to destroy it.
3043: Contact lost with the Outworlds Alliance due to Clan Invasion.
3044: Clan Invasion hits Draconis Combine/Federation border and begins marching towards Terra. Clan invaders cut through most resistance without issue. The sole major win is when the Combine saves Galedon V by challenging the Falcons to a trial that they would never again return if they lost, and captured numerous Elemental suits to study. ComStar secretly aids the Clans, while trying to get them to destroy Hanse Davion, and the other Houses as well.
3045: Clan Wolf captures Robinson and continues on. Smoke Jaguar/Ghost Bear/Nova Cat invasion of New Avalon is defeated in a long hard battle, with the Kell Hounds and Wolf's Dragoons helping to turn the tide. Upon learning that the Clan's ultimate goal is to capture Terra, ComStar challenges them to a trial on the planet of Galtor III. ComStar wins, though suffers horrendous casualties. Clans are forced to a 15 year truce. Operation Scorpion, an attempt to Interdict Hanse Davion from the HPG network, fails when targeted Davion strike forces remove ComStar controls. Anastasius Focht runs a coup in ComStar and begins to secularize the organization.
3046: Many ComStar members leave rather than secularize and form the Word of Blake. It finds many homes throughout Star League as many factions dislike Hanses' rule.
3049: Jade Falcons prepare to violate the Truce of Galtor III and have Ulric Kerensky removed from his post by claiming he sabotaged the war and effectively killed a generation of warriors. Clan Wolf engages them in the Refusal War and the Falcons are shattered. Ulric dies though, and the Wolves are briefly absorbed by the Falcons before being reformed under Vlad's command. Natasha Kerensky does NOT die to jump jet to the head. Sorry guys.
Phelan Kell leads the Warden Wolves to Outreach where begin rebuilding.
3050: Victor and Omi Kurita are married, and the plates at the ceremony have the names of numerous planets taken by the Nova Cats and Smoke Jaguars on them. Everybody invited knows what that means and are not surprised when, in his toast, he gives those worlds to his son and daughter-in-law. Victor Kurita-Steiner-Davion and Kai Allard-Liao heroically lead the Star League forces against the Smoke Jaguars, while turning the Nova Cats to their side. The Ghost Bears counterattack into the Smoke Jaguar Occupation Zone, and the war heats up. Kitsune Kurita-Steiner-Davion is born, heralding a new future for the Star League.
3051: Casualties mount on all sides, but with the Nova Cat defection, and the Ghost Bears hitting all parties in a bid to expand, the Jaguars take the heaviest tole. By the end of the year the Jaguars effectively cease to exist in the Inner Sphere, though the Ghost Bears have expanded their territory and are much harder to kill off. On Christmas day of 3051, Hanse and Melissa Steiner-Davion die, victims of an exploding flower pot. Victor Kurita-Steiner-Davion becomes the new First Lord of the Star League. Kitsune Kurita-Steiner-Davion named the new heir to the throne.
3052: Katherine Steiner-Davion blames Victor for their parents death and removes the Lyran Commonwealth from his rule. She calls Lyran troops home, cutting off most of the reinforcements he's been using to fight the Ghost Bears. Thomas Marik and Tormano Liao also remove their support from Victor, annulling the engagements of Peter Steiner-Davion with Isis Marik and Tormano Liao's son (does he have one in canon?) with Katherine Steiner-Davion. Within months, isolated fighting begins between Lyran and Davion forces, often sparked by Word of Blake agents. Ghost Bears sit back and begin digesting their gains.
3053: Tormano Liao and family killed in a palace coup and Sun-Tzu Liao rises to the throne of that realm. He and Katherine Steiner-Davion announce their engagement as the FedCom Civil War begins to wage in full bloom.
3054: Capellan Confederation and Free Worlds League invade the Sarna March, already in the flames of Civil War, and retake much of it. The remainder collapses into total chaos.
3055: Black Dragons attempt to kill the Coordinator and begin an open rebellion using the discontent caused by Victor's attempt to use Kurita forces against the Lyrans. Jade Falcons and Wolves begin raiding into the Combine and Federation, taking advantage of the discord in those realms. Clan Wolf-In-Exile and the Wolf's Dragoons engage both Clans, limiting their gains. Free Worlds League, happy with its gains, attempts to sit back and begin the digestion process, though it is forced back into the war by Word of Blake agents. Confederation continues attempting to retake former worlds from the Federation.
3056: The Star League Civil War is in full bloom, with all member states pulled into it by Word of Blake agents acting in secret.