Binko, surely you haven't missed all of the talk about Honey1? That would seem to fit your specs pretty well.
I think also that this board is filled with facts that undercut the notion that Chicago tastes are geared toward the jello rib. North side baked ribs a la Twin Anchors and Barnelli's are a well-known phenomenon, but the South and West Sides (hey ,that's 2 out of 3 of Chicago's sides) are jello-free zones where the meat is cooked in aquarium smokers.
Your three recos, along with Honey1 are nice North Side examples of BBQ. I would also add Smoke Country House, Leon's on Ashland, and Hecky's of Chicago as places that try to be real BBQ, as opposed to baked jello-rib places, but all three are just awful in my experience.
(The Leon's on Ashland absolutely does not serve jello ribs; they serve tough, dessicated, heavily worked-over ribs that were partially smoked at some Leon's commissary then re-heated at the Ashland store. I had high hopes for the place before it opened, because a couple of the S. Side Leon's aren't that bad and the Ashland store is set up to smoke -- it just doesn't and never has.)
In the end, I would much rather eat the semi-jello ribs from Biassetti's than the smoked-but-awful stuff from, say, country house where the ribs are par-cooked, partially smoked in an electric smoker, then placed in the fridge and re-heated in a frying pan full of bad BBQ sauce upon ordering.
Biasetti's ribs were always tasty, and they improved markedly when Larry Tucker was there after NN closed. Whatever he did remains. They seem to be a hybrid of baked-jello and smoked, not unlike Carson's -- which does apply smoke contrary to popular belief. Just don't call the ribs BBQ. That's what Honey1 does. Don't get me wrong, when I BBQ, I BBQ. And I prefer BA, Lem's and H1 to any jello rib. But Biasetti's is a nice peccadillo, especially after you throw in the relish tray, cheesy potatoes and creamed spinach, all exemplary. Which leads me to a...
KANKAKEE REPORT
The fact that it's really BBQ doesn't mean it will be good. I recently took one for the team in a big way by touring the BBQ shacks of Kankakee. (Had to be there for work.)
Wrightway BBQ is a perfect looking little smokehouse that offers the standard ribs/tips/links/wings setup of the South and West sides. Problem is, the meat is quite obviously boiled first then finished with a light smoke. Not inedible, but no where near most of the Chicago spots. Link was more like a small, hot frankfurter than a Chicago link. It reminded me of what they call in PA and parts of NJ a "Texas Tommy."
Soul da Soul is a neat place that seems to be a community anchor. Absolutely huge BBQ and fried foods menu. I tried some tips and a chopped pork sandwich. More boiled-first, smoke finished action. Aslo, no seasoning whatsoever and the smoke was 100% Kingsford briquette. Really not good. I still very much enjoyed the place and the people, and would bet that the fired stuff (chicken, fish, shrimp) is better than the cue.
Now then, on the way back from KKK, I stopped for a beer at this German Biergarten-cum-roadhouse in Peotone. The place rocks. It's like Resi's or Laschett's-meets-Rt. 66 Biker Bar. It's a few minutes off of I-57, and well worth a stop. Huge garten with a big fireplace. Hackpeter and beer. Don't think too hard about the big German WWII weapon collection above the bar.
http://www.peotonebierstube.com