Sounds like a Bronco then. The larger tubes (3.25" diameter by any chance?) are the "truck" size, where the cars were 3.0" diameter.
Only the '66 Broncos still had the fill plug in the housing and no fill in the chunk/3rd member. After that there were no truck housings that had any opening in the housing other than the vent on top.
A 3.50 was probably not that common on passenger cars, but it was the base gearing for all the 4-wheel drive trucks. If it's a stock bronco still, it's got 28-spline axle shafts and we can compare measurements on the chart we have for axle lengths of the various years.
Another thing with the truck housings is the big-bearing and small-bearing ends. With yours sounding like a small-bearing (better for a car anyway I would think).
Here are some bolt patterns for the housing ends/backing plates for the Broncos:
https://www.wildhorses4x4.com/category/bronco_rear_axle down near the bottom right of the page you can see the diagram in the section for the retainer plates.
There were very slightly different length axles (based on brake offset) for the different Bronco models too.
I'll go measure my spring perch width if nobody comes up with an answer. I've seen it here hundreds of times, but as said I never remember them!
I could be wrong, but I thought all 9" rears had the hump in the back after a certain year. The smooth back was a throwback to the old 8" housing probably, but I've never researched it. It was probably a necessity for the trucks with their often lower gear ratios.
You can still buy the smooth centers (or at least you could a few years ago) from places like Currie Ent. for doing religious restoration, or if you just like the smooth look as many hot-rodders do.
Personally I like the hump because that's what I'm used to, and I believe it adds some structural rigidity to the housing overall. Not necessarily a deal-breaker for a lighter car, but for a race car or heavier truck, the added strength would be a good thing.
Paul