Almeda Riddle, Texas Gladden, Horton Barker (these are voices you have to get used to) all sang songs of this tradition. Buell Kazee, Clarence Ashley,(East Virginia) and of course Jean Ritchie carries on this tradition (as well as the Ritchie family from the Cumberlands). It's a marvelous musical style that is often not understood by new interpreters.
Peg Seeger knows about this style too. "Wedding Dress" for example. Or Hally Wood's "Saint James Hospital". The "modal" thing is speculative. Were the so-called Church modes employed by these traditional Appalachian songs? The jury is out on that one.
Check out Texas Gladden singing "I Never Will Marry". "Cousin" Emmy singing "East Virginia Girls".
Then there's the "House Carpenter", many versions of "Barbara Allen" that precede the popularization by such folks as Joan Baez.
The connection with the ballad style of Northern Ireland and the Scottish Border becomes apparent when you hear these old-time ballads.
"Lord Randall" has some interesting variations as well.
When you bring in the conventional chord structure of the guitars and some banjos (though many tunings were used to incorporate the old-style tunes), the original unusual quality of these old style songs were lost into the stew of early "country music". This is what Cecil Sharp was complaining about and he may have had a point.
Early "country" music has it's own quality, though, differerent from what we're talking about here.