This is what you need to do. I bought a Hellwig front bar through BAC @GMachineDartGT and had the same issue, after some back-and-forth Peter noted that the sway bar should be close to parallel with the strut rod at ride height so I flipped the brackets around. The angles are still a bit off and the top bushings rub on my adjustable strut rods but it definitely works. I would move the brackets out farther and weld them to the LCAs but then they'd be getting tight with the big ol' single-piston brake calipers at full lock. Maybe when I upgrade to modern Mustang brakes I'll do it idk, I'm sure it'll firm things up a bit more having the links vertical like they're supposed to be. Could flip the calipers to rear-mount but I don't feel like tearing down the whole front end to swap spindles from one side to the other.
Btw I HIGHLY recommend a rear sway bar. Putting one on my Duster made it feel like the wheelbase was shortened by a foot the whole car is so much more responsive in cornering, doesn't feel like the rear wheels are being dragged around against their will anymore. I'm running 275-wide Continental ultra-high-performance tires in the rear so grip isn't an issue, even on the stiffest setting (which I leave it at all the time) for the rear bar I've never felt like the car wanted to oversteer. It's just about neutral now tbh. Might have to go down a setting when I get a working LSD in the rear though.
