I unfastened both lowers on my El Camino while leaving the uppers connected and it still made me jump. The car was on stands and the diff was supported by a jack in what I thought was a "normal" position.
I think when assembling I'm going to attach the lowers first since they're nearly straight and it should be easier to line up the second bolt after starting the first. The uppers being at such an angle just makes things difficult- you adjust up and down using a jack that moves on an arc and can roll front to back but not side to side.
I also think the springs are complicating things for you- since they're not 100% perfectly straight vertical they're moving things rearward. The rear swings on an arc so your springs will curve slightly as they compress. I'm assuming that the bolt was removed while the car was elevated somehow but it'll be under some sort of pressure/twist any time the car isn't resting at ride height. This seems like a situation where removing other parts and fasteners might actually save some time over fighting the single one you wish to remove, although I would have done the same thing. I recently went through a similar situation with my exhaust where I fought it both ways because I didn't wish to remove every single piece.
I propose that the easiest way would be to unbolt the lower shock mounts and remove the springs before wrestling with the differential at all. I could see me fighting to align a C.A. mount much longer than that would take. I'd even consider removing the driveshaft if the C.A. bolt(s) were to be removed again as it provides more resistance to any adjustments in addition to two springs and shocks as well as bushings that are being articulated. You had to fight half a dozen things to line up the bolt holes.