Hi NM,
This is a very complex question indeed. As a 340 operator myself with more than 6000 hours on A340/A320 we are talking about a similar piece of kit. In fact the brakes are exactly the same. Yes the brakes are fantastic but they are very susceptible to damage if you do a max stop from a reasonably high speed. The other point to remember is that the true brake temperature takes about 5 minutes to be reflected on the indication due to sensor location.
Regarding you concern about brake fire spreading beyond the wheels. Next time you are under the aircraft, have a good look at the space around the wheels and you will aggree that it is unlikely that fire will spread beyond the wheels. What is of more concern is the possibility that debris from failed wheels or brakes may have punctured the wing fuel tanks above (as in many previous accidents).
Now your concern about getting the aircraft pointed into wind. For the A330 (A340) and other similar large aircraft that I have operated it is critical to first get the aircraft stopped as per SOP's. Now to get the aircraft pointed into wind is another thing that takes time. Time being the commodity you can ill afford in a real emergency. May I recommend to you that it is far more important to stop exactly on the centreline for a very good reason. Usually runways slope away from the centreline, thus if you do have a fuel tank punctured then fuel leaking to the ground will flow away from the fuselage. For your information I have tried to practice pointing into wind and I have found it unsatistactory for many reasons. One is mentioned above but another is the fact that you will now have the nose of the aircraft pointing at and maybe close to the runway edge. This will now cause evacuation problems but more importantly cause difficulties for the fire crews as the first strike for these emergency staff in case of fire is from the front of each main wing. This may now not be possible.
Regarding your various questions about brake temperatures etc. The answer is basicly answered by Airbus in FCOM 3. If you do a stop from above 100 knots it is serious. The degree is based on what brakeing you used. If the reason for stopping is not serious and you quickly released the auto MAX brake and used only low brakeing, then I see no problem with any decision about what you might opt to do subject to brake limit temp. If you used MAX brake to stop from above 100 Knots, then thats it - stay stopped. Don't move the aircraft regardless until you have been externally inspected and have a clearance that is is safe to do so. I have physically inspected brakes that were used to stop from about 120 knots using auto MAX and they were completely destroyed. Even trying to taxi the aircraft would not have been safe if at all possible. By the way it is not recommended to put anything but cool air on carbon brakes without risking total destruction of same.
Re the stop/go question - definately NO. Just leave the gear down after take-off until they cool down (unless you have an engine failure)
So in summary, stay on the centreline, stop, sort out the problem, and only when you are completely happy that it is safe to do so (preferably after an external inspection if in any doubt), then taxi off the runway. If it is a single runway airport, then all I can say is "you can't help bad luck" but you and your passengers have priority and safety is the priority.
If you want to read a very good accident summary on this subject especially on the things NOT to do, just look up the British Midland Rejected take-off accident many years ago now.
I hope this gives you something to think about
Have a nice day