This has got to be the most derailed thread I've ever read. Buffy, Picard/Riker relationship, Star Wars, cats!?!
I think Riker would have ultimately gotten the crew home though probably not as fast as Janeway. He'd know he'll need Chakotay and merge the crews with him and B'elanna in their respected positions. I almost want to say Tuvok would have been his commander but Chakotay was an instructor for an advanced Starfleet course and Tuvok would be more suited at tactical. I also believe Riker would correct B'els attitude more stricter than Janeway, similar to how he dealt with Ro with the occasional Bat'leth spar. I think Tom would have been an ensign starting off but would have been promoted later on along with Kim. Janeway wasn't really disrespectful to the Doctor but Riker would have been more respectable IMO, with his dealings with Data. Q would have stopped by but I don't think he would be as enamored with Riker as much as he was with Janeway. Q would more likely make fun of him and comment on the fact that if he didn't give up his Q abilities, he'd be home. I don't think Seven of Nine would have made it to the cast. Riker wouldn't have decided to make a deal with the Borg until after he gets caught trying to cross their space in which case he'd comment on how badly Species 8472 is beating them and that he found a way to stop them (Harry would have still been hit by one). We also would have saw at least one deflector beam that he used in Best of Both Worlds part II. We'd probably see Riker, Tom, Kim, and Chakotay play poker. He'd probably split Tuvix, taking Riker for a needs of the many fan. Neelix wouldn't have been the moral officer, simply a guide and later, the cook. I'm assuming Deanna would have been a crew member (with her going with him in Nemesis) and she would have been the ship's counselor/moral officer. Riker would probably let Kes be Kes.