My guess is going to be major surgery for something like that - the next question is why? (2012 300 HP 6 banger I could understand)....but it's a lot of work for something that won't net any gains I can think of? If you think mileage is it - I'd rethink that honestly. Get an AOD and a stockish 289-302 and you will be money and time ahead.
Don't want to be a wet blanket, but...
Suspension wise, there's absolutely nothing that will interchange in bolt-on fashion. Serious fabrication would be involved to install the Mustang suspension in the Cougar. If you're going to that kind of trouble, there are much better suspensions designs to start with than Fox-body Mustang.
Seriously, you'll get better results for much less trouble and expense by simply rebuilding the existing suspension with top quality components, and incorporating a few of the proven tweaks from Shelby and the Boss 302 chassis manual while you're at it.