Your stock struts in the front combined with the large stock rear bumpstop in the rear is probably whats causing your car to bottom out.
Now that your car is lowered, your stock struts in the front may be too long, and will actually compress far enough to cause them to bottom out. Not only that, but your stock bumpstop in the rear is too tall, which will also cause the car to bottom out with aftermarket springs.
The above can be solved by getting new bilstein struts in the front (completely getting rid of the stock shocks) and getting a newer, lower profile bumpstop. We sell the Maximum Motorsports pinion snubber here.....
http://www.stangsuspension.com/store...?idproduct=609 You can use this on the rear to help prevent bottoming out.
The sagging is probably caused by a faulty Eibach Pro-Kit. We have seen Eibach springs randomly sag in the past. It is more common with Eibach Sportlines, but we have seen this happen with the Pro-Kit as well.
The above can be solved with newer springs. I'd get something that does not lower as much, and has a bit stiffer spring rating. This will assure no sagging will take place, and restore your ride quality. Here is the link to the Steeda Sport Springs...
http://www.stangsuspension.com/store...p?idproduct=61
Please let me know if you have any more questions...
Sincerely,