I haven't found that finishing a game quickly enhances the score much at all. In fact, what I have been doing lately is extending the length of my games to increase the score. What is more important, is establishing your dominance of the galaxy as quickly as possible, rather than actually finishing the game quickly. I almost always go for military victory, as the scoring for any other type pales in comparison. I turn off all other victory types, and also turn off surrenders so that I can end the game exactly when I want to. I wage nearly continuous war until I have eliminated all but one enemy planet, but the score wont be nearly so high if you end the game at that point. Extend the game for another 2-3 years to get a higher score, which if you are playing just to win the game is pretty boring, but if you want more points it definitely works. The time it takes to actually do this is not long, as at that point all my planets are built up, poplation on each planet is maxed out at 20B (23B for homeworlds), I've built my military starbase array, and I'm not moving any fleets or ships at all. It is definitely a case of diminishing returns though, and past 3 years or so (depends what's happened in your game), I havent found that your score increases very significantly. It's mainly just a matter of hitting the turn button a hundred times or so. I always end the game on Dec 15th of whatever year I decide to finish in, which will help your score a little bit, rather than running over into the next year.
One thing I ignored for a long time was the Spin Control Center, Military Starbase Array, Omega Defense System combination. These three things together will increase your military rating by an amazing degree. Late in the game I design a huge-hulled ship maxed out with nothing but weapons, purely for the purpose of putting them in orbit around the planet with the SCC. With the MSA you can have that planet be in the radius of effect of 16 military starbases maxed out with components to augment whatever type of weapon you have on those huge-hulled ships in orbit. I make sure the weapon type is the same as my combat ships so that my extra inactive fleets can go bask in the radisu of those starbases too. This is the most tedious thing I do to augement score...
I also make sure I finish the entire tech tree, which supposedly gives you a score bonus, although I've never tested it out to see how much it might be. If you finish the tech tree before you plan to end the game, dont decrease your research spending. This will lower the overall technology score you will earn.
Towards the end of the game, when I have it down to one enemy planet, I build a maxed-out influence starbase next to their last planet, then gift it to them. This will prevent any culture flip, and again let you end the game when you want to.
In the latest game I played, the settings were huge, abundant or common everything, masochistic. I started in the dead center of the galaxy and had the great fortune to have a Precurser factory ruin on my homeworld. This let me expand very quickly in all directions, grabbing at least 30 planets in the first colony rush. Very early on in the game I was the largest civ in the galaxy, which proved to be very beneficial for my score. When I had the first opportunity to end the game, I did so just to see what score I would get, but planned on reloading and playing longer. At about 10 years, the initial score was about 115,000, which would have been the best I had ever done before, but I was shooting for much higher. I reloaded and extended the game another four years, letting my population max out, finishing the tech tree, and watching my economy grow. The end result was a score of just over 150k, which only took about an hour more of actual game time to accomplish.
There are certainly more advanced techniques than I use, but these work well for me, and for the level of micromanagement I want to spend time on.
I dont know of the Lost Fleet series, but maybe I'll check it out. Another book which comes to mind that I cant remember the name or author (sorry!), is an alternate history where the American Civil War was fought to a draw, then another civil war happens 20 or 30 years later with the same results, and then again in another 20-30 years. The book is set during this period, which coincides with WWI in our own reality. Tanks are just being introduced into warfare (being called "barrels" in that reality), and on one side are the Northern USA, Imperial Germany, and a few other allies, and on the other side Canada, the CSA, England, and various other allies. I really wish I could remember what this book was. Anybody know?? I searched around a bit today and couldnt figure it out...
edit: I think I found it... American Empire by Harry Turtledove, who writes a lot of great alternate-reality fiction.
Sentient species taste better...