Ken -
Big subject, and there are a lot of people much more experienced and knowledgeable than me to chime in at some point.
If by emergers, you also mean cripples, you are off to a good start. They’re kind of the same thing, for all practical purposes, but how you fish them can be distinctly different.
Soft hackles can be fished just about any way you can imagine to do it, as long as they stay in the water !! Upstream and deaddrifted as you would a nymph, without an indicator. Or with an indicator, maybe in the form of a dry fly with the soft hackle trailing it. And down and across, on the swing, as you’ve suggested.
Soft hackles can range from extremely simple little things to something more complicated. The simplest one I’ve used is one I fished yesterday for rainbows in one of our mountain streams. It is tying thread for the body and a starling feather for the soft hackle. The fly that triggered this pattern for me is a bit more complicated - the Water Cricket, which has a simple embroidery floss body, ribbed with the tying thread and using starling for the hackle.
This is a Water Cricket tied by Jeff Hamm of Auckland, NZ. It has caught trout everywhere I’ve fished it since Jeff sent me some a while back.

The soft hackle that was best for me yesterday was basically a simplified pheasant tail nymph pattern - forget the weight ( read beadhead ), wingcase and legs, just substiute a soft hackle after tying and ribbing the body and adding peacock herl for the thorax. It took fish when trailing a dry fly and when fished down and across. If you fish it that way, let it hang at the end of the swing - probably get more hits at that point, and as you start to pick it up than at any other time.
Partridge and orange is a favorite and classic soft hackle fly - one of many. At least as many permutations and combinations as there are body colors and types of hackles to use. That’s why it’s a big subject.
Partridge is a favorite for the soft hackle. But hen, pheasant, starling, brahma hen and all manner of other feathers are used. The point is simply to have a rather sparse bunch of flexible and flexing feather barbs moving around suggesting that something alive, and edible, is at an appropriate level in the water column.
Can’t speak to your particular waters in the N.E. But I think you can probably just start off tying a dun for the waters you fish and stop when you get through the abdomen and think of finishing it off with simple thorax and a soft hackle rather than wings and hackle ( whether traditional dry fly or parachute style ).
Didn’t get around to fishing them yesterday, but I did tie some down and dirty soft hackle coppery johns. “Coppery” so no one takes offense at calling this creature by the name copper john. Down and dirty because there was no wingcase, no expoxy, and no legs - just tails, a copper body, a peacock herl thorax, and some grizzly hen hackle. I’m confident it will catch fish if presented properly.
Well, that should get you started thinking about soft hackles, and, hopefully, form a base for others to challenge and build on.
John