2004 v6 Mustang: Max A/C Issue.

OK, let's see if I can answer some of your questions. The AC heating system is very difficult to access behind the dash. For repairs of anything beyond the bottom of the ducting, requires the dash to be removed.

Is it possible that a foreign object has gotten in? I once had a car that I swore smelt like oak burning when the AC was started. When I finally got around to fixing it, I found that the blower motor was overheating. As I got into the job, I found the cowling covered with oak leaves. The leaves entered the system and got into the blower. Add heat, and get a burning oak smell.

Could the burning smell be anti-freeze?

If this were my car, I would take a look at is the blower motor resister. It is located at the bottom of the passenger side (right hand) duct work (near the glove box). Possible there is contamination on the element. Check for water or anti-freeze (heater core leak).

Next, look at the blower motor itself.

While there, check that the dampers move as expected. Switch to defrost mode, does the air re-direct to the windsheild? If not, look at the vacuum line from the engine bay through the firewall.

Anyway, that should give you something to start with. Good luck.