It is a little tricky to diagnose an issue like this without driving the car, but it does sound a lot like bump steer that you are describing.
All stock Mustangs bump steer. Power steering cars tend to insulate you from the feel but if you change tires, or go to wider wheels the car still reacts with bump steer more pronounced.
Going from biased ply tires to radial tires right there will start to make the bump steer more apparent.
If you lower the upper a-arms be advised that it increases the bump steer and even with the Shelby 1" drop, you are close to putting the ball joints in bind.
Going to manual steering is going to accentuate the entire situation.
Recommendation is 1) NEVER install a rear antip-sway bar in a Mustang. Even with a small one, you will tend to increase over steer, sometimes to the point of what is now called snap steer. That is a sudden violent oversteer on the car.
Cars with leaf rear springs do not benefit from rear anti sway bars regardless of what anyone tells you. You will not find them on any of the Shelby factory built race cars. PERIOD.
2) You should install a bump steer corrector kit on the car. You can do without them if you use the modified tie rod ends made by Cobra Automotive. It is difficult to completely eliminate the bump steer. Everything effects it. No two cars are exactly alike. On some it is terrible, on others barely noticible.
3)Install ball joint wedges if you lower the car and if you go that route, the 1" Shelby is not the ultimate relocation.
Actually 1-1/2" is but back in the day that would have required special ball joints or the above mentioned wedges.
A safe compromise is actually 1-1/4", but again you need to use the wedges.
The actual number that your car will be lowered in relation to ground clearance will vary but it is closer to 1-1/2" in the front. You can use spring spacers on top of the front coils to bring it back up. A lot of people find the car a little weird driving after lowering because of the rake. That is all personal taste. Your mileage may vary.