Exhaust leak. Just solved the same problem last week. When you decelerate, the extra air gets sucked into the exhaust and makes little doof doof popping sounds. Get down and tighten the header flange bolts and look for obvious things like cracks, etc.
I also had the thump under the car problem. My crossmember was partially rotted out on the passenger side and the "tube" portion of it that accepts the bolt had broken away and the x-member would whap up against the bottom of the car when you did something that would "flex" the drivetrain like punching the gas. Make sure that nut and bolt on the center of the crossmember hasnt broken off. That would also make the transmittion wobble and whack up against the bottom of the car. They break off sometimes. I broke one on my last stang.
The final thing that could cause that is if your dump valve for the airpump is malfuctioning or not opening. That would pump air to the cats fulltime and that would cause some exhaust backfire. Check your EEC for a code.
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91 GT Carb conversion, holley 600 double pumper, edelbrock performer intake, FMS "C" drop springs, march 1000 underdrive pullies, crane 1.7 roller rockers, GT-40P headers, bassani x pipe, american thunder catback, FMS 4.56's, msd aL6, trunkmount battery, A/C eliminator kit, 3000 stall tci streetfighter, AOD with transgo kit, A+ servo, 300M hardened lockup shaft, kevlar bands and 28,000 gvw trans cooler, 3 core radiator, 300 lbs stripped with a full interior
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