This is pretty long. I hope it helps you catch more fish. It's just another arrow in the quiver.
I have had fairly consistent success short leader fishing using split shot on my tippet on faster flowing broken water. Riffles, and around rocks, and structure, in plunge pools, and through various lanes in depths of 1.5 to 5 feet or more. I fish facing upstream, and cast upstream. I use a 10 foot 4 wt. I fish nymphs, eggs, or SJW, tied onto 3 to 5+ feet of 6X tippet in turn tied to a 12-15" length of yellow Amnesia indicator (I have 25# - just cause that's what I have) which then is fastened to another 4+ feet of 15#+ mono before connecting to my fly line. From fly to fly line my leader can be 10 feet or more. It's kind of a bastard czech style, as my fly is not always weighted. The small diameter tippet allows the split shot (a very small #8 or #6) to quickly draw the fly down into the feeding lane.
I cast upstream, and keep my tip high, and lead the current downstream, keeping the line fairly taut and the Amnesia visible (either in or out of the water). The Amnesia acts like a coiled indicator, when it hesitates ... I lift, and either have the fish, or the bottom. I find it's a great sighter and its sensitivity allows for most takes to be noticed before the fish spits the lure. Some may argue that I'm fishing the sinker, and do not see the take, but I would suggest the sinker only gets the fly into the feeding lane (yeah, sometimes I get the bottom muck and have to clean it off, but to me that just means I at the level I need to be - yes I lose a few flies.)
I seldom have more than 5 or 6 feet of actual fly line out of the tip of my pole. I cast into the closer spots first, and then move progressively through the further feeding lanes, before moving upstream to the next section. With the broken water, I can get fairly close to the fish (or fishy water) without disturbing them - coming up from downstream helps keep it subtle. The longer rod allows for a fair reach, and allows for drifts further into the current that may pass by my position and extend a bit downstream.
As for braided leaders, I've never used them. But I would think for nymphing that the leader's bulk might induce drag and inhibit the ability of the tippet to sink to fish level. The smaller tippet, especially if fluoro - I use copolymer usually - allows minimal drag, and faster descent. Then again, if the braided leader ends above the sighter, drag would not be an issue and may improve casting.
Weighted flies eliminate the need for split shot. Bead head PT's, Y2K's, work well especially if tungsten.
Amount of weight depends on flow. If flow is strong and deep - use more weight. Sometimes I fish with a dropper - but often get frustratingly tangled and soon abandon that idea and return to a single fly.
That's my present nymphing style. I hope it helps you catch more fish.