You have two choices:
Troubleshoot, find and fix problems.
Throw parts at it until you either run out of money or get lucky.
The first approach is cheaper and more productive. The second method is expensive and is a pain in the wallet. Always fix what you know is wrong first, because sooner or later you are going to have to fix it anyway.
The 24 lb Cobra MAF is a mismatch for the computer's internal program. It seems to ban-aid and cover over some of the basic problems you have.
The MAF body and sensor are designed to match each other. Therefore you can't swap sensors between different part number MAF bodies and maintain proper calibration. The assembly is designed to match the computer’s internal program, and swapping a different MAF can upset the computer's calibration. In other words, yourCobra MAF won't match the calibration of your 5.0 Mustang computer.
The only other MAF that is a one for one swap for a 93 and earlier 5.0 Mustang is the 94-95 Mustang MAF.
94-95 Mustang GT MAF - $40-$100. It is 70 MM instead of the stock 55 MM on regular stangs built prior to 94. It uses a slip on duct on the side that goes to the throttle body and a 4 bolt flange on the other. You need a flange adapter to fit the stock slip on air ducting that goes to the air box. Wiring plugs right in with no changes. *1 *2
Once your replacement 70MM MAF is in place, disconnect the battery for about 10 minutes. When you reconnect the battery and start the engine, the computer will relearn the settings for the new MAF.
*1.) Metal flange adapter
http://www.kustomz.com/cat3.html Buy the TR70 for $44.95. Or spend some time on eBay looking for one that may fit.
*2.) MAF & sensor interchange
The 94-95 Mustang 5.0 MAF & sensor is also found on:
1995-94 Mustang 3.8L F2VF-12B579-A2A,
1994-92 Crown Victoria 4.6L F2VF-12B579-A2A,
1995-94 Mustang, Mustang Cobra 5.0L F2VF-12B579-A2A,
1994-92 Town Car 4.6L F2VF-12B579-A2A,
1994-92 Grand Marquis 4.6L F2VF-12B579-A2A,
Evidently the –A1A, -A2A, AA, etc. on the end of the part number is a minor variant that did not change the operating specs. You should be able to ignore it and have everything work good.