Total control would require me to re-write months of previous WWF programming to prevent it's own storylines from interfering. Since that's going too far I'll do my best to work with what they gave me:
First things first, I would not have run it as an invasion storyline at all, by 2001 there had been a change in the presentaion in the mojor federations whereby it was much harder to see guys coming in as athletes who had worked their way up through the minor leagues to earn spots on the big stage, instead they were clearly employees. Instead I would've brought in as many big names as were available from the start which would probably be limited to Booker T and DDP initially (possibly Jarrett as well) with people like Hogan, Savage, Luger, Steiner, Nash and Hall coming in as soon as possible.
Once I had 5 or 6 big name stars (especially the ones who'd already been huge in WWF prior to the Attitude Era) I would begin to put them into the big PPV spots instead of those who'd actually won the Monday Night Wars for Vince (and some sort of deal would be struck whereby a percentage of their merchandise sales would go to the WWF guys to make up for the loss of PPV money, got to keep my own guys happy). Initially the WWF guys (Austin, Rock, Jericho etc) would still get chances but over a period of 4 or 5 months they would dry up and we'd end up with PPV cards dominated by the WCW talent.
Re-enter Shane McMahon. At some point following his WM feud with Vince he would've disappeared, now, with Survivor Series approaching he would make his return, still a shareholder in WWF. Upon his return he would bring 3 or 4 of the best young lower card WCW guys, a few WWF guys who he'd had past kayfabe friendships with (Test and Big Show for example) plus a few of the buried WWF stars (Austin, Rock, Jericho etc) to re-ignite the family feud with him as the babyface. The promos would be shoot-style, not to the extent that WCW's were at the end but certainly close to the knuckle and based around Vince repeating the mistakes the Bischoff and Russo (not by name) had made. This would result in scuffles backstage, interference in matches and (not quite) cross-promtional matches which would be much more heated than normal. A 5-on-5 elimination tag would be made for Survivor Series which Shane's team would lose (he'd be the manager btw).
With the battle lines drawn the 2 factions within WWF would continue to feud and, due to a further influx of talent including Sting, would now have a slight advantage. Sting would win the Royal Rumble and head to towards a WM18 match with WWF champion Hulk Hogan meaning that, regardless of the result, Vince would retain control of the championship. Between the Rumble and WM18 Sting would turn face and join Shane, this however would not be enough to turn the tide his way.
One factor I haven't mentioned yet is Paul Heyman and ECW. This was deliberate since I want them to be the X factor in this angle. Around the time that Stings turns on Vince Heyman would turn up with 4 or 5 of the biggest ECW guys that hadn't already been signed by WWF, I'm thinking Dreamer, RVD, Sabu, Sandman and Steve Corino, all but 1 of whom former ECW champions and well known to the WWF fanbase. I would spend a couple of weeks teasing which side they were on, they'd had ties with WWF which had been mentioned previously and Heyman always hated WCW but, on the other hand, he's never been a fan of the old guys retaining their spots which is what WWF would now represent. He would pick Shane, tipping the scales going into No Way Out (or whatever it was called back then) and the upcoming WM18.
At WM18 control of the company would be up for grabs. Sting would defeat Hogan with the Scorpian Deathlock to claim the WWF title, forcing Hulk out of the company in the process, a number of others would have their final matches as well. Vince would accept the occasional on-screen role of WWF President (with no real power), Heyman would become WWF Commissioner and we would move into the Ruthless Aggression Era with a new generation of talent.
