Pretty sure the Cat 3 Single limitation when eng out is more related to HYD redundancy.
Ie You need all 3 HYD systems to be be Cat 3 dual.
Thats why on 343/5 if you loose eng 1 or 4 you can be CAT 3 dual,(as you still have 3 sys) but eng 2 or 3 you only be Cat 3 single.