V6 Stock Exhausts have ZERO rumble to it. It is more than likely aftermarket. If you don't see two pipes out the back and just one, they may have just changed the driver side stock muffler. Get under the car and take a look. And welcome to Stangnet.
+1 Spend the money you would on the repairs towards another used GT. I sold my 96 V6 5peed for $3500. Unless you are dead set on owning that car for life, junk it.
Do you have experience working with vehicle electrical systems? If you do it wrong, you could end up frying the radar along with part of your vehicle's electrical system.
Check the vacuum hoses running along the firewall to the vacuum tree which should be on the driver side of the engine bay near the firewall. Sounds like you may have a leak.