I'm pretty sure you'd have to junk all of the stock wiring to go with a fuel injected engine because the stock system i believe is a 6 volt system instead of a 12 volt system, so i don't your lights, gauges, etc. would work properly. It would probably be easier to go with carburetion because you'd have to do ALOT of rewiring. You might be able to stick with a 6 volt system if you stay carbureted. The best option in my opinion would be to rewire the car (if in fact it is a 6 volt vehicle) and to go with fuel injection because you'll get better gas mileage and great throttle response.
Now that i think of it, the fuel injection system from that 85 cougar is probably Throttle Body (CFI) so that system is crap anyways and you'd have to do alot of adaption to get later model fuel injection to work.
If you're on a budget, going carbureted would be ALOT cheaper. Good luck, that sounds like an awesome project you have there.
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Mustang Parts Specialties ripped me off, it could happen to you as well.
'84 Mustang 5.0 LX
my LX
'89 Mustang GT
my GT