All "worm and ball" style steering boxes will have a small, on-center dead spot. Just part of how they work. Now, that said, it should be pretty small. As steering boxes wear it increases, and worn steering components- tie rod ends, pitman and idler arms, even worn suspension bushings and ball joints can make that feeling worse. Loose steering box bolts would definitely make that feeling worse, as will any cracks in the K frame at the steering box mount. Those cracks are not uncommon.
So, before I say it's something that you should get used to, it's worth making sure you don't have any worn or damaged parts first. But even with all brand new parts and a solid K frame that play on center will not be zero.
I haven't done much of anything to lower the rear of my car. Most of it is just the AFCO leaf springs I'm running. They're 121 lb/in, "zero arch" springs. Factory mopar springs for these cars are pretty close to flat when loaded, they sat pretty low in the back already. I did replace my leaf spring hangers with a set of leaf spring sliders, and my bracket to do that lowered the rear of my car about 3/8". Not much in the grand scheme of things.
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Other than running springs that don't raise the back of your car (like the super stock springs do), your best bet for lowering is just a set of lowering blocks between the spring and spring perch. Cheap, easy, and if they're 1" or shorter no real dramatic changes in suspension geometry.