Sounds like its time to switch to a T-5 and toss those AOD boat anchor, horse power robbing, no gear shifting fun, pile of complicated crap in the scrap yard.
Seriously though, how many miles does the OP have on the AOD? If the TV cable is in working order then it could be the direct clutch pack or the direct input shaft is broken. A lot of guys in the past have gone to SilverFox (http://www.silverfoxtrans.com/) for help so I would start there. If you want to stay automatic then my suggestion would be to move to a 4R70W and a controller like Baumann Controls / US Shift (https://www.usshift.com/usq4.shtml). Swapping over to a T-5 is not as easy as it used to be as they are just not that plentiful as they used to be.
Run Motorcraft plugs and dump those pieces of shit in the trash can. Buddy ran them once on his old Fox Mustang and it ran like a turd. Put new Motorcraft plugs back in it and it ran like it should. Had several other guys say the same thing. Not sayin that is the issue but they do not seem to perform to well on our cars.
So I do not remember what mine looked like on my '83 as I cut it up when I went to a carb and got rid of the pump. All I wanted with the fuel sender to work as the tank is sumped. Here is what I found on Cool Cats:
The part number for the fuel tank sender for and '83 is on there but the only one I have found is on ebay and it is waaay expensive and has no provision for an internal tank pump. If you look at the '84 is says only serviced with pump which leads you to another part number and it can be found for a decent price:
It appears to have everything but I think the tanks are different between the model years 83-84/85 and 85/86-88 in that 85 appears to be a year in which the change was made and my guess here is that the external/internal fuel pump went to an internal only pump and this may have also been when the tank size was reduced. Not sure if this will affect you one way or another but I would hope that your tank would be the right one for the part on ebay.
Anyhow, check out the link to the one on ebay for an '84 and hopefully it is the correct one.
I know for a fact that the MM panhard bard will clear 2.5" factory path tailpipes (Dynomax and Flowmaster are known to work well) with 275's on a Fox Mustang. My Coupe has MM torque arm, panhard bar, Griggs coilovers, and 275/40/17 Nitto 555R's in the rear and the Dynomax 2.5" tailpipes clear. I saw one 3" setup but the guy custom built it with mandrel bends and tig weled everything so it was like looking at artwork.
Being this is all on a Mustang there may be some nuances with a Bird/Cat but my money is on it fitting with very little work. My guess is that the path of the tailpipes will be identical to the Mustang. The 3" tailpipes on my Bird are Flowmaster mandrel bent units for a Mustang LX that were lengthened only in the part that hangs down and runs to the back of the car past the fuel tank. I believe we lengthened them around 8" or so.
Anyhow, keep up the good work and I wish my projects moved like yours.
Swap the 8.8 out of the Mustang into the Bird and get the correct offset wheels to match the Mustang rear end. It will move the wheels inboard 0.75" on each side and you can see this by dropping a plumb bob off the top of the rear fender and measure back to the center of the existing wheel on the existing rear end. Install the Mustang 8.8 and put your stock wheel back on and do the plumb bob again and that will tell you exactly how far in the wheel has moved. From this you should be able to select the correct wheels. If you want to go five lug then get the axles out from a 94-98 Mustang V8 or V6 rear end and that will swap you over to five lug, disc brakes, and it will just about be the same width as the stock Bird rear end (+/- a 1/16").
Gut the EEC-III out of the car and start over on wiring the new motor. This is what I did on my '83 with the 351W and it is carbed with an MSD ignition and distributor.
Put the motor and trans in the car from the Mustang. Put the car up on jack stands such that the suspension (front and back) is loaded and also safe to work under. A four post lift is the best but you will need to make these decisions based on your safety. Install the yolk from the drive shaft into the trans such that it is bottomed out on the tail housing seal. Measure back from the center of where the U-joint installs into the yolk to the face of the flange on the rear end that the DS bolts to. Whatever this measurement is you want a minimum of 3/4" less than that on the length of your DS. This allow for compression into the trans and for the yolk to slide back out of the trans for rebound. This is how the shop that built my aluminum DS told me to do it and it worked great. Here is a site that a lot of folks trust to build custom shafts and how they want you to measure for a DS:
Would the Fairmont and Zephyr compare better to the 80-82 Birds? I know a bunch of the Fairmonts have been raced through the years and at 105.5" on the wheel base I thought they may share some of the same metal from the firewall back.
Both of the racks in my cars are off SN95 Mustangs so dimensionally they are identical however the spline on the input shaft of the SN95 units are way different so do not go that route unless you want to buy a hybrid shaft from Maximum Motorsports or make your own. The other issue is that the SN95 inner tie rods are the same thread as the Fox inner tie rods however the threads that the outer tie rods screw onto are metric on an SN95 inner tie rod and SAE on a Fox inner tie rod. I used Fox inners and outers but some have used the SN95 inners and outers but shortened the inners. The Fox Mustang rack will bolt into our cars with zero issues. Some say that you have to match the pump to the rack ratio but I find that to be a bunch of BS.