I was also a dedicated Glass Dome Hickory Pit guy, where we went nearly every Sunday night. What I liked about the ribs were that they required a good gnawing and tug, they could be prepared well-done ("burnt like bacon" was how I would order them; my father asked for his "incinerated") with no sauce (on the side only) and that the slab itself was a well-trimmed entity consisting of alternating struts of meat and bone, with no floppy, flappy top meat or other awful and fatty distractions.
As such, I, too, have long been in search of a Hickory Pit replacement. I continue to mourn its demise, and have even driven by on a couple of occasions hoping against hope that they re-opened but somebody forgot to tell me (all hope was lost when I saw on my last drive-by that the even the building was gone.)
My two closest approximations: Gibson's (make sure to tell them not to cut up the ribs, something they tend to do) and Rosebud Steakhouse on Walton.