Check the gaps between the rear tires and the front edge of the wheel-wells on both sides with a ruler. If they are not within 1/8" of each other, it will cause the rear end to wander as you described. Some with the BMR brackets have noticed a difference in this measurement after their install as well. If this is your case, contact Kelly at BMR and he will help you fix it. Don't worry about your UCA, it only controls the pinion angle.
Current Mustang: '14 GT/Track Pack/6spd-sold
Previous Mustangs: '68 Coupe, '73 Mach 1, '89 GT,