This an interesting puzzle with insane consequences.

The only thing I can think of is that the shots degrade quickly with temperature, and that the bad lots (severe outcomes) were ones that had better cold storage during transport and administration.

I do not think the converse would be true; poor storage temperatures make them more deadly, as heat generally messes things up. How stable are these lipid nano particles and adenovirus vector vaccines?

I guess the Janssen one only needs refrigerator temperatures; so my theory does not work for that one. Could there be another mechanism for degradation of effectiveness?