Talking snare drums in particular......If the shell was a constant, is there a chart anywhere that shows what different edge types on what side would produce what result? Even maybe with the bed being another variable?
I think bearing edges make less of a difference on snares than toms. Meaning: you will have a harder time hearing the difference between a rounder edge and a sharper edge, especially if you muffle.
Rounder edges will give you a more muted note; sharper edges will give you more ring.
Snare beds are advised - how deep is a matter of preference. I personally do not like really shallow beds.
I'd focus on finding a builder who can do really good edges & beds. They are like hen's teeth.