Another idea, if you haven't tried it, is to put their pads in a litterbox, and train them that way in addition to outside. I think having a box where they have to enter into it to wee or poo, helps distinguish between your rugs and potty pads.
Mine are all litterbox (with washable pads), indoor grass, and outside trained, and haven't had issues with them going on the carpet since they've been fully trained. Having a male who likes to lift as high as possible, I am thankful for the higher sides on the litter box
Going back to the beginning and starting his training over, would probably be helpful. Also, neutered males can be markers too. And you mentioned you moved into a new apartment, that change alone, can trigger new bahaviors
