Robin, congratulations on contributing to the debate! I would be surprised if varying the mass for the explosion in a 2 WD merger scenario did not lead to a variation in luminosity, though maybe the mass range is not significant. I thought there was a lack of good quality measures to any great distance where Type Ia’s are used, but I must admit that I’ve not looked into this in great detail.
Andrew, I think there might be difficulties in getting supernova explosions in core collapse supernova models but not a WD that reaches the Chandrasekha mass limit. I have a recollection of reading somewhere in the past couple of years that modelling revealed that certain stellar mass ranges could lead to explosions while others may collapse to a black hole without creating a supernova.