The worst part of an Empire playthrough

I'd advise you against blasting stuff with the Death Star. It'll just decrease loyalty on your planets, swing more into the Rebel camp, and hurt you in the long run. In the future, I'd advise you to use a small galaxy setting- that's what I always play on, because as you've said, it drags horribly if you don't.

 

To find the Rebels faster, assemble more fleets with fewer ships in them. I like to call mine "exploration fleets." The ship strengths vary, but by and large I send an SSD, two ISD IIs (both with full fighter compliments), and troop transports so that I have sixty troops going in overall. I don't put any characters on board unless I have a bunch to spare, and then I send them out to the unexplored regions and drop troops off as needed to take over planets. I choose the number sixty so that, in a ten-planet sector, I can take over any and all Rebel planets without defenses in that entire sector.

I actually enjoy playing on Huge galaxy right up until the point where I've secured the Core sectors. After that it's a bore-fest

Maybe I am alone in my desires...but I don't really mind having to search for the rebel base. More often than not I wind up taking control of almost every planet in the galaxy before I take out the rebel stronghold (even in the large galaxy setting). One time I even reverted back to a prior save when I had accidentally assaulted the HQ and ended the game .

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."