IMO the key is to start exploring/colonizing from the very start of the game. You know after you capture the two leaders that the base is going to floating around out somewhere on the rim (or possibly the core), so there's no reason to put off getting a foothold out in the rim. I use imperial probe droids a lot early in the game to see if I can find any rebel presence out on the rim, and if so I try to take over that whole sector (although usually they're gone by the time you get there, if they detected the recon mission at least). Also try to build small fleets with lots of troop capacity for colonization. Especially in the end game, you know they aren't going to have resources for a lot of ships, so there's no reason to go out there with a SSD and multiple Imp IIs. Really all you need is a Victory (I or II) and a bunch of assault transports, maybe a Carrack or 2. The reason I say Carrack is that all 3 of those ships mentioned have a 60 or less hyperdrive rating, so they can really move out there, and that kind of fleet can easily handle a few starfighters, or a nebulon-B or something. I few Assault Transports are almost as good as a lancer with their laser rating. So yeah, start colonizing early, and in the end game send those fast fleets around dropping troops, assaulting neutral planets if you want, or just send your diplomats all over the place. If you control a lot of the rim by the time you've got the two leaders, then the base won't be as hard to find. With this strategy I was recently able to win on day 858, huge galaxy, expert difficulty I had all but 3 core planets and most of the rim controlled, and the base actually ended up in the core. I haven't played Rebellion in years, so I don't remember if this was typical for my empire games or not. Note that my playing style is pretty obsessive...I have the game on Very Slow for most of the time, making sure every single resource (construction yard, shipyard, training facility, personnel, fleet) is always engaged in something useful if possible. It takes a while and you do a lot of "move to slow to bump to the next day and then move back to very slow to take care of everything."