I don't have an answer but want to say that the design of steering geometry is all about going forward, not backwards. So, that might be the problem right there. If the lower ball joints are somewhat loose perhaps they stay in their socket under normal forward driving but the forces generated by backing up cause them to move.

As most people know when a car turns the outside wheel follows a wider arc than the inside. This is the Akerman effect and the compensation is designed into the steering geometry. Because the Sunbeam Tiger went from the Alpine steering box to a rack & pinion the position of the rack was far from optimal. The Akerman is so bad the outside tire turns in more than the inside.  As if that wasn't bad enough when backing up at full lock one tire is almost dragged sideways. The forces are so great that the lower A-Arm fulcrum pins have been known to break! I'm sure the forces in the Pinto aren't that bad but I said that to illustrate what can happen in the extreme. The wider than stock tires may not help your situation. Hopefully others can give you more insight.

I found the source of the pop/clunk..

Jacked up the passenger side wheel, removed the wheel and discovered that the 50 year old upper control arm bushings are deterriorated and need replaced..

So im adding that to the maintenance list.

Anyone have any suggestions or tips about removing the old bushings and installing the new ones..