I'd go with the 1" bars. You'll notice a HUGE improvement in handling, and the downside is fairly limited. Mopars were seriously undersprung in the front to begin with, they really NEED larger bars even in stock form. Sway bars are a good addition too, but you don't want to mismatch too much by trying to fix all your handling ills with just a sway bar. Sway bars are great, but keep in mind that they also act like a spring and can make for some interesting handling if you have a huge bar, they can cause some interesting "twitches" when they unload if the sway bar isn't matched well with the torsion bars.
I have 1.12" bars in my Challenger and love them, definitely a stiff ride but not harsh at all. I know, not an A-body, but realistically the suspension is pretty much the same, the E-bods are just heavier (hence the really big bars). That being said, the 1.12" bars on my Challenger maxed out my torsion bar adjusters, I was riding pretty much stock height or maybe even a shade higher with no adjustment left, I ended up getting Magnumforce 2" drop spindles to solve the problem. Something to keep in mind, it shouldn't be a problem with 1" bars but any larger than that and I would suspect you might notice the loss of adjustability in the ride height, especially if you like your car set up low.