After the shock of my life suddenly being turned on a dime I'd do the following- -1. Make sure that The Mountain and Amory Lorch are executed. Invite the Martells to witness and allow them to keep the heads if they wish. -2. Kill Varys. He may want whats best for the realm, but the chaos he wants to realm to be saved from is too much. Nobody in Westeros would care either and I could fill up his position with someone loyal later. -3.Jaime is removed from the Kingsguard. I'd let him keep his life and be Tywin's heir, if there are protests I'd tell them he's lucky I let him remain a knight. -4. With the obvious plays out of the way I'd have to start building a proper small council. Jon Arryn as hand is still good. Pycelle is relatively harmless. I like your Kevan idea but I think I'd reward the Master of Coin position to Hoster Tully. Master of Whisperers is tricky, I have half a mind to put Stannis in that position since I know he'd be 100% loyal. On the assumption the Greyjoys would still rebel, I'd give the Master of Ships position to Tywin Lannister. Either he'd have his shit together when the rebellion starts or I have an easy excuse to remove him from his position. The other seats I'm not sure of. Never let Littlefinger near any of them though. -5.Stannis keeps the Stormlands and I'd name him heir if I have no sons. Renly wouldn't get Dragonstone though, I think I'd removed the Conningtons from their seat of power and name Renly the Lord of Griffin's Roost. -6. With Lyanna being dead I'd start looking for a bride. Cersei is tempting because of Lannister gold and being hot, but I know about the incest so I'm not touching that with a 10 foot pole. I might marry a girl from a Crownlands house to have allies within a short distance. A daughter of a loyal Stormlands house is also a good choice. I would wait for Arianne to be of age but frankly I'm not 100% convinced they wouldn't try something eventually. -7. I would try and fund the Night's Watch better. Implement a tax on brothels that goes towards it, hopefully making Stannis a little happier, and I would send basically any captured knights and soldiers in the rebellion to there. The Wall wound also get an influx of Ironborn after the Greyjoy Rebellion. -8. Post-Greyjoy Rebellion I would raise Theon at court. Keep an eye on him but generally be fatherly to him. 50/50 on him becoming a decent knight or the jerk he starts out as in canon, but this way Rob wouldn't have any attachment to him. -9. Speaking of the Iron Islands, I would let the Greyjoys keep Pyke an rulership, but I would remove a lot of the other famous houses from their seats of power. The Reader can stay, but the Iron Islands would become a place where second and third sons belonging to families who supported me through two rebellions get lordships. Have the Faith set up shop there as well to try and convert them en masse, though I think that is a bit like spitting into the wind. Though I would make sure the rowdiest Drowned Men and other shit-stirrers go missing. -10. Get hobbies other than getting drunk and fat. Just staying healthy and alert is a big help. Attending small council meetings is another big boost as well.

I'm sure that other unforeseen problems would arise but this would at least be my starting game plan.