Jordan
In your description you mention a number of different symptoms. These may be unrelated to your heater core problem, and as such just add confusion to troubleshooting your problem.
Regards the heat shield under the console being missing, I doubt this is the case. It does not have to be de-mounted to work on the transmission, is not in the way of anything, so nobody would have a good reason for removing it.
In normal circumstances the auto transmission runs very hot. It's hot enough to require the heat shield to minimise heat leakage into the cabin. In your case it is bound to be worse. When your transmission is failing there is extra slippage, which causes more heat build up, which radiates into the cabin via the console area.
In addition to this you are mentioning black fluid on the dipstick. It's the job of the transmission fluid to conduct heat out of the transmission and "lose" it via the radiator/cooler externally. When the oil breaks down it no longer does this job effectively, and this is why transmissions fail, the clutches get burnt up by too much heat.
Long story short, you will be experiencing significant extra heat from the console area because the trans is failing.
dcb is correct I would think. Your coolant leakage into the car is most likely caused by corrosion in the heater matrix or the pipes inside. You would need to attend to it quickly, losing coolant is bad news. Unfortunately you will have to strip out the dashboard to get at it. There is great information in the How To section on the aircon system
AIRCON. Read through this, it will give you an idea what to expect round about pps 21-24.
Joe