lol, sorry, I'm laughing at your location. Where are these evil speed bumps located? I live in Flower Mound, therefor, drive in Lewisville often. I noticed you have a 95, I have a 94. And I know what you mean about having to make a complete stop over the bump then roll down for each axle. I have the same problem too. And duh, you're suppost to slow down, but you shouldnt have to make complete stops like you're doing now.
You may need new struts, because I do. My car rides rough, and I have the same problem with speed bumps and with the same stop and roll solution as you. Theres a little test you can do to see if you need them. Push down on your car, and lift up. If it comes up fine, you dont need new ones. If it comes up, and bounces, like once or more, you need em. I noticed this occurs to my back, but have yet replaced them.
What I believe you are brushing is what I believe is something for your oil pan. I dunno, but its a metal thing that is way lower to the ground than a stock mustang body. In the mean time, you can either stop and roll, like youre doing now, or take the speed bumps, still slowly, but at an angle. Also, you may want to find other routes.
For an example: You live in Lewisville. You know the strip mall that has Best Buy, Toys R Us, and other such things? Well if you are entering via Round Grove Rd, dont take the first strip mall exit. Those are for the special people. Stay in the right lane, so you can pass those people. Then get into the left for the next turn. They made this parking lot lane far away from the entrance as possible for a reason. You see, everyones after that first exit. And due to speed bumps and pedestrains (especially at Toys R Us) it gets backed up, and is typically slower. If you go my way, not only is it faster, but you avoid every single speed bump. You have stop signs, but very few considering the number of speed bumps you avoid. Then again, you can always be a jerk and cut through parking lots to avoid them, but for this particular area, I suggest this route.