School me: 63-66 Dart vs 67-72 Dart suspension

Before you blame the suspension for that, might it have been the tires?
When the rear ride height is lowered, the springs are fairly flat, and on the street you will be hard-pressed to feel anything but sidewall flex, or possibly a little loosness in the rearmost shackle bushings......IMO.
Again, on the street this is no biggie.........IMO

I occasionally run 325/50-15s BFG-DRs in the stock 68 Barracuda tubs, with nearly flat rear springs, and with the "3/4" inch offset hanger kits. You cannot get a pinkie between the sidewalls and the tubs. But there is enough room that I can zoom around 90*corners,in the city, at 30 mph, with quite a bit of power being put down, with just an occasional mild rub. You might not want to underestimate the semi-elliptics quite so fast...........IMO.

Totally agree with AJ here. With a zero arch rear spring there isn't a whole lot of side to side movement if all the bushings are in good condition and everything is installed properly. A lot of people do full suspension conversions because their cars handle poorly, when really what they needed was to rebuild the suspension and ditch the 14" rims and old worn out tires.

You can go further and replace the rear shackles with a set of spring sliders, pretty much takes all the side to side flex out of the rear mount. That's what I did on my Duster, in addition to running zero arch springs (there's a little arch not much though). Any lateral movement would have to come from the springs themselves. I run 295/35/18's on the back of that car, and there's very little lateral movement in the back when cornering. I don't have more than a 1/2" of clearance to anything back there, and I've never shifted anything around enough to rub when cornering.