Hmmm, the cougar may be different, but I didn't have any real trouble changing mine out.
Look and see if you have a "relief" pressed into the frame above the brackets. If so, you can use a open-ended box wrench to slowly back the bolts out an eight of a turn at a time, then rock the bolt/bracket around and you will get the bolts loose. The bolts closer to the front of the car are easy.
Otoh, if you just loosen the subframe bolts about half an inch, you'll get all kinds of room to work.
hth,
dan
