Alt Country/Folk, American roots

A hundred thumbs up for the Matraca Berg recommendation. She's a very talented writer and singer who released a few albums years ago and then dropped out of the Nashville scene, for quite a while except for session work (check out her harmonies on Oh, Cumberland w ELH on the Songcatchers soundtrack, or better yet, her singing lead on that song, which I believe she wrote, on The Dreaming Fields. Her work never quite fit the Nashville mold and so some of the old stuff is a bit overproduced, but if you like Dreaming Fields, check out The Speed of Grace and Sunday Morning to Saturday Night. Most highly recommended.

I'll also give a shout-out to Shelby Lynne's baby sister, Alison Moorer. If you can find it, her duet of Picture w Kid Rock is outstanding.

Check out Amanda Pearcy (singer/songwriter from Austin).
Esp. 2nd CD, Royal Street.
Disclaimer: some personal bias at play here, but it's great stuff.

A lot of good choices so far (Hiss Golden Messenger being my personal favorite among them), but there are a few names that I'd add.

First - since the OP mentions Uncle Tupelo/Son Volt/Wilco among his reference points - I'd suggest a quick listen to The Bottle Rockets. Tom Henneman was a guitar tech and "non-member" of Uncle Tupelo and I regard Bottle Rockets as the third "nephew" band. They've done some great stuff over the years (I'm a sucker for sad songs and Waiting on a Train is my gold standard for hard rockin' weepers). I'd think this is close to a "can't miss" recommendation given Todd's stated preferences - although I've been wrong before.

Two other names that immediately come to mind are 16 Horsepower (picture Uncle Tupelo as channeled by a bible thumping hillbilly on psychedelic drugs) and Alejandro Escovedo. When Escovedo was really on his game (roughly 1992 to 2005) , I'd argue that his output held his own with anyone's. An A list name for sure.

Straying further from rock music, Townes Van Zandt is also worth thinking about. Like Escovedo, I think Townes best material is is truly timeless music.

Oops - Brian Henneman of Uncle Tupelo/Bottle Rockets. His brother, Tom wrote "Waiting on a Train" IIRC.

Doug Seeger, Going Down to the River, 2014