Ah, Angels of Light... lovely! Absolutely fantastic project that I much prefer to any other Gira-related thing. Especially 'Sing Other People' I find totally magnificent. It's a great record, not only for the material/individual songs, but also how over the course of itself it seems to grow ever darker. Wonderful, wonderful music. Also very fond of the split with Akron/Family, a band which occasionally ventures into something that suits your descriptors in their own right, but just as often does not. The AoL/AF split is great, AF material is very intuitive and wild (but very musical). Great stuff;
http://www.youtube.com/watch?v=kvmeTiswnyE - but definitely not what you're looking for.
Seeing the descriptors (and veering a bit away from James Junkin, which is fascinating but which reminds me of little more than some Nick cave material... - just my limited frame of reference), I'm thinking of a couple of things - one of which indeed was Jandek. Dingy, dilapidated, lurchy - it's all that. I'd agree it doesn't necessarily have a 'Southern' sound to it, but it fits all your qualifications quite well. Definitely worth digging into, I'd think.
A record I think absolutely fits the descriptors is Smog's The Doctor Came at Dawn. Smog/Bill Callahan has recorded a lot of material, and a lot of different stuff (he once started out extremely lo-fi, even made it onto Garbage Sandwich!) and now does more general folky country. What you could call his 'middle ages' harbour some material that comes close to 'dingy, dilapidated' music, and The Doctor Came at Dawn is the prime example. It seems quintessentially Jandek-inspired, but more musical. Some great cuts:
You Moved In: http://www.youtube.com/watch?v=MARBOVCSkwQSpread Your Bloody Wings: http://www.youtube.com/watch?v=b8156uxBESkEverything before was more 'eclectically' lo-fi (great as it is), everything after became decidedly more polished, sometimes annoyingly so, up until the beautifully pure A River Ain't Too Much to Live. It is by far not dingy and dilapidated enough to suit, but it's a wonderful record to try anyways...
Let Me See the Colts: http://www.youtube.com/watch?v=qohDy0UT1G8Perhaps even more suitable (?) to your inquiry is Will Oldham, now the much lauded and fairly mainstreamish Bonnie Prince Billy, back then the decidedly rawer and more interesting Palace (in many guises - Palace Music, Palace Brothers, simply Palace...). His discography up until '97 (from thereon it was Will Oldham, and then BPB, with some exceptions) covers a lot of musical ground, some of which may be right up your alley. Debut record There Is No One What Will Take Care You is very raw country (country noir is what is was dubbed back then, I think; not my favourite record, so not too much input from me here). Follow-up Palace Brothers/Days in the Wake is another record that seems very Jandek-inspired (right down to the cover art) and which is raw and shaky and wonderful:
You Will Miss Me When I Burn: http://www.youtube.com/watch?v=g_KIJGCqZz8No More Workhorse Blues: http://www.youtube.com/watch?v=hqzwaLzjdvUViva Last Blues sounds much drier and Southern (Steve Albini produced it), is my personal favourite, but is by far not as dingy as Days in the Wake. 1996's Arise Therefore is absolutely marvellous, very lo-fi and with an added drum computer. It sounds very detached, very raw, very unstable, very imperfect, very amazing:
Stablemate: http://www.youtube.com/watch?v=KUIJ10P6TpQGive Me Children: http://www.youtube.com/watch?v=cwnJMcXAmxcYou Have Cum In Your Hair And Your Dick Is Hanging Out: http://www.youtube.com/watch?v=ZEo0Ij8-OS8Songs: Ohia may be something you'd like to try. Again, different records have wildly different sound, so depending on what you try you'll get different results (Didn't It Rain - gospely; The Lioness - rockish; Magnolia Electric Co. - pure country rock), but the record worth trying most is Ghost Tropic. It has a very sticks-and-stones sound, some percussion like it were twigs, dry strings on the verge of breaking, and an atmosphere that is sometimes almost suffocating, oppressive, stifling. Great!
The Body Burned Away: http://www.youtube.com/watch?v=Ib6pUL5t8okOcean's Nerves: http://www.youtube.com/watch?v=g2vbN47KEXcHope anything takes your fancy - this is the music in my collection that I rank among Angles of Light anyway, for varying reasons :)