Slight wallowing during corning......

Are you drag racing it? For drag racing the slant six bars can be used with the super stock springs for wieght transfer during launch.
If that 245/60-15 is a MT Sportsman or something like that, some of what you feel may be in the tire.

Other than for drag racing, yes the 340 t-bars will be better, and the sway bar will help with body roll in cornering.
Not knowing the shocks - its hard to say what they are matched to control. Try the larger bars and see. That's generally easy change unless they are stuck.
That's a pretty small tire up front and the rear is tall. That and the SS springs in the rear put more rake on the car which loads the front even more.
Say roughly 12.4" radius front and 13.3" radius on the rear. Almost 1" difference in ride height. :eek:

With the SS springs, for street use, I'd recommend going up to at least the largest factory t-bars, or .990 or 1.03 aftermarket. Should be able to find any of those second hand if you're not in a rush and have time.

As far the lower control arms tabs, you'll have to look at them. If original to the car, unlikely to have tabs unles the anti-sway bar was ordered as an option.

Then yes, definately need larger tires to handle the additional loading. Anti-sway bars load the outer tire even more during cornering. Its their one draw back, and is outweighed by their benefits.