Uke's center was the fulcrum and I was essentially bracing the bottom half while trying to wrench uke's top half over that point. Often, there would be a slight lifting element needed to get it to work. Which means that, even if you start out moving around, you eventually stop to execute the technique, which in turn stopped and planted uke. This comes out most obviously with hip throws, but I noticed it happening with other students and things like the gari throws: they weren't reaping so much as planting their foot and trying to push uke over their leg. Same thing with hiza guruma: stop his knee and pull him over it.
And one of the most important parts of doing that is not to stop moving. This sort of method may seem more obvious with versions of a throw where you (as tori) are advancing and uke is going back. That's actually where I started to notice this, doing an advancing harai goshi.
Eventually, I began to see the gari throws this way, too. Uke's shoulders are going back at the same time as I'm reaping his leg. It spins uke like the propeller on a plane, with his center as the pivot point.
Even hiza guruma started to feel like this, although I'm not sure how I can describe it in words.
Here's a hint: getting this result usually requires a "tick tock" sort of balance break. For example, if I want to throw him forward, I load a little weight (not much) into his back foot. The throw, then, happens as he recovers back forward: connect to his center and spin him like a propeller. Same thing if he's going forward: extend him a little more forward than he intended to go and when he straightens back up, reap his legs out from under him.
Done right, it feels (to both of you) like you didn't do anything, like he's weightless. Of course, I'm still working on it, but when I do hit it, boy, it's exciting.