Rear Sway Bar?

I installed an after market sway bar on the front of my '65 Barracuda but the rear end feels like it will come loose on hard higher speed turns. I told the club's Barracuda expert that I am thinking of installing a rear sway bar. His comment was installing extra rear spring leaves would work better than a sway bar. Is he correct?

if the rear end feels like it’s going to come loose, that is an over-steer condition.

DO NOT stiffen the rear roll resistance (rear spring or rear sway bar). Add more front roll resistance (thicker sway and/or T-bar)

the video below is what happens with too much rear resistance at high speed cornering. My rear sway bar has been disconnected ever since. Might be ok for lower speed handing. But not 70+ mph curves. Especially a dog-leg with a bump accelerating into straightaway.

Every car combination can be different. Make adjustments to what you feel.

fast forward to minute 1:39 then play