How to get rid of understeer in a 1970 340

Do you have a posi-trac diff? If so, and if the diff is tight, it will very much tend to push the front end straight ahead under power (and somewhat even under coasting) when the rear tires have good traction. (I have to be careful with diff tightness for RWD rallying on gravel; too tight, and if the rears hook up at a spot, it is straight ahead towards the trees...yikes!)

Have you ID'd your tire brand/model? That would help to know. Soft sidewalls will make the ride good but add to pushing with a heavy front sway bar. Are there any scuff marks up the sidewall, even a little bit, after the front end 'floats'?

The KYB suggestion was for low cost with something at least decent; I won't gainsay any others' experiences with them; they are not top performers. As said, you can do a lot better with Bilsteins. Yes, Koni's are still there, but for general use on regular road surfaces that go up and down and have some surface roughness, I have found Bilsteins to be much better. Koni valving has always seemed to be focused towards road racing surfaces and parking lot auto-x'ing, and seemed to me harsh on regular road surfaces even when adjusted towards the soft end. Anything that is going to have some good performance valving is going to be a bit harsh feeling, IMO.

ANd, BTW, my thoughts on rear anti-sway bar size are just off the cuff based on car wieght and somewhat heavier rear springs, not calculated or anything like that. So take it for what is.