Sorry - I missed your additional post "suitable alternate just below".
If your high level logic is to effectively wait for some kind of 'quorum' from the multiple aircraft monitoring systems before deciding that you have a "serious event" then as 7373 indicated, you leave yourself open to the risk that the ability of these (other) systems has itself been compromised by the fire.
Press-on may well be your chosen course of action, knowing that the incident is real, but you chose to press on becuase you did not consider it to be truly a valid alert (no ECAM confirmation).
If you have a single alert for the most serious event you could face in an aircraft, would you not agree that the course of action that is best is the one that gets you on the ground as quickly as possible. Other factors (firefighting ability of airport etc) are secondary?
P.S. I am not un-calm, and greatly respect your integrity in making the post in the first place.