Running games based on works of fiction can be very tricky. You have to decide very early on what your approach to canon is going to be. Is the plot of the books inviolate? Are the PC's inserted in place of the 'real' protagonists? Are they bit players doing their own thing while the protagonists of the book go off and follow the plot? Any of those can work, but you need to have a grip on what you want.
For example, if I were running a game set during the War of the Ring, I might have my group be a group of Rangers and other goodfolk opposing some ancient evil Sauron's raising in the northlands - or some other place far away from most of the action. They might hear about a disturbance and Black Riders in Bree, but wouldn't be directly connected to it. They would make a vital contribution to the war, in other words, but wouldn't intersect with Frodo's quest.
Creating your own setting gives you - and, crucially, your players - much more freedom of design. Personally, since I greatly enjoy worldbuilding, it's the option I prefer. However, if your players don't know the setting, it might as well be a homebrew setting as far as they're concerned!
When you've got a setting that spans centuries, like the world of Ender's Game, it's much easier to slot PC's into the picture. Of course, if you do things that way, you're pretty much guaranteeing that Ender Wiggin will not be a going concern for the story - but it's just as well, really. Recycling protagonists is much more problematic than recycling the setting.
Why do your players veto the Ender setting? Even if they liked the books, they might not want to game there - I kind of think I wouldn't want to myself. The setting is not hugely interesting in itself, and frankly we don't see much of it. The interesting bits we do see are backwaters where Ender is staying, being problematic. :) If you want to stay far away from him, you might as well be creating your own setting anyway, because you'll have to make up tons of stuff from scratch.
"All right, I am not the Shadow. You have nothing at all to worry about. Except, oh, wait, I'm pointing a gun at you."