I can pretty much guarantee you're bottoming the suspension out over every single bump. That's why it rides like a train car going down the tracks, because just like a train car you've got no suspension at all when you're bottomed out.
You could raise the car up with the torsion bar adjusters to test this theory a little bit, but even at stock ride height you'll still bottom out those /6 bars. Maybe less frequently. Problem is that if you raise the suspension substantially with the torsion bar adjusters you'll throw your alignment out of wack too, so, it won't handle right anyway unless you also get a new alignment. And then after all that you'll still find out that you need new torsion bars, so, you'll be doing another alignment after you install those.
As for the larger bars making the car stiffer, yes and no. Yes, they will make the ride stiffer. But, the problem you're having with the car isn't stiff torsion bars, it's a bottomed out suspension. Your current bars are so soft they're not doing anything, and you're riding around on the bump stops. Stiffer bars will keep the car off the bumps stops, so you'll actually be using your suspension.
I'd be inclined to say you should go up to at least a .89", if not a .92" torsion bar. Usually I don't recommend anything less than 1" anymore, but it sounds like you've got a very stock car, so those would probably be more of a change than you want.