1. Did you replace the cap with an OEM from Ford? Don't use a Stant or aftermarket cap. The parts guy will likely swivel in his chair and grab it from the shelf behind him because it's a high failure item. Same cap used on Ford trucks BTW.
Make certain the threads on the coolant tank aren't stripped. That's one reason why you don't use an aftermarket cap except in an emergency. The ones I have seen do NOT have the tighten till it clicks and slips feature and people tighten them down like the hammers of hell and strip the threads on the tank.
I just replaced my cap and it was like $12.00 from Ford. Mine was seeping.
Make sure the rubber gasket on the cap is free from debris and the old rubber gasket from the old cap didn't get stuck on the coolant tank.
Boiling over coolant is almost always either a blockage or overheating.
Put the front of the car up on jack stands or ramps, take the cap off the coolant resovoir and run the car until the thermostat opens. Squeeze the radiator hoses and "burp" the baby
If that doesn't work, just as a test, take the thermostat out and run the car without it.
If you still have problems, then you are looking at a blockage which is probably in the radiator.
One last thing, I'm not sure if this is even possible on the Mustang but make sure the hoses are not reversed.
I had this on a Volvo and it drove me nuts.
It was actually possible to reverse two hoses and the coolant was flowing against itself causing this exact problem.
Keep us posted!