I could see there being issues caused by having it cut off like this, just by the o2 sensors possibly reading too much oxygen, and that could be messing with the fuel curves. Given I'm not an expert of the newer Broncos and multiple o2's of the 96, but aren't there post cat o2's on the 96??? I had bought my 96 new, so it had no issues when I had it, but the 86 I'm restoring now gave me all kinds of fits from the o2 sensor (single) being messed up, and the wiring being corroded & not getting a signal back to the computer.
I'd say get that exhaust back together and re-evaluate, until then you've introduced too much unknown into the system to possibly diognose anything properly. That may be all it is, but get the exhaust back on and report back.
Yeah no problem, we're all just figuring it out as we go, im sure your ears will thank you once the exhaust has a muffler again, just be sure to put all the o2's back on in roughly the same areas they were when stock. Then you can pull codes again if its running funny, but something tells me it's just a bit confused on what to do with the downstream o2's off.
I'll leave the 1996 sensor stuff to the guys with more knowledge there, cuz its out of my wheelhouse, but fear not, there's a ton of knowledge these guys have on how to make it all work, it's out of my league, but I'm sure someone will chime in on here to follow up more.
Just a bit confusing how your piecing the story together in multiple posts.