There are several posts in this thread (I just read this for the first time now) that cause me concern.
First, the pics of your car depict Coy's C67 wheels which, if I am not mistaken, are 17" x 8" with 4.75" backspacing. If they are indeed that configuration, there should be no reason correct factory upper control arms and ball joints would come close to making contact with the wheel rim and no reason for wheel spacers. The fact that this appears to be a real concern leads me to question what upper control arms and ball joints were on the car before you tackled your front end project?
Second, shims on the upper control arm mounting studs are found on pre '67 Mustangs. They should not be needed or used on the '67 for alignment purposes. Their presence on your car raises red flags for me.
Third, the difficulty in getting the correct lower control arm installed on one side should not be an issue unless the frame components are damaged.
For these reasons, I would suspect the car was smacked hard enough to damage the front frame and suspension at some point and whoever repaired it cut corners and used incorrect parts to get everything to "fit". I suggest that a close inspection with a tape measure and the frame alignment specs drawing would be a prudent step to confirm that all front suspension attachment points and the shock towers are within spec.
As far as the 4 link and other high end "solutions" to the ass-wiggle issue your friend is experiencing, I suggest that before he throws parts/money at the problem, a thorough inspection of what he has would be appropriate. For example, the rubber bushings at the front end of the leaf spring wear out over time that may result in too much play in the front mounts. Another example is the rear leaf spring shackles and shackle bushings. Again same issue on the bushings. On the shackles, some aftermarket extended shackles intended to compensate for sagging rear leaf springs can twist when torque is applied resulting in a side to side wiggle.
There is no such thing as "Standard" air shocks for '67 Mustangs. The rear upper shock mounts are a thin piece of sheetmetal not designed to carry the weight of the rear end of the car. In some cases the sheet metal flexes to the point that it tears rendering the upper mount unstable. Last but not least, sloppy or short cut repairs to the rear frame rails in the past may have loaded or unloaded one side of the car creating an unstable platform. Unless the car will be seeing track time, the cost/benefit ratio for a 4 link is hard to justify for many folks. Tape measure and frame alignment spec drawing might be helpful in determining if this is an issue for your friend. Putting the car on a frame alignment rack would allow both front and rear structural alignment to be determined. At that point the problem(s) are identified and repairs and upgrades would be easier to determine.