As most cats he's also attracted to the mysterious smells of cupboards and closets
"An open cupboard door? That's an invitation for..."
"...some more thorough inspection"
At least it's too full of things to let him get completely inside (not that he wouldn't want it.) Of course it helps to know that he's very clean, but "a man's cupboard is his castle". Perhaps it's time for an "act of God"*?
*as described here an "act of God" for cats means creating some unpleasant noise or other disturbance for the cat, without him knowing it comes from you. If he connects the mischief with the unknown disturbance (thus "act of God") he may be more reluctant to repeat it. Plus, he will not loose his trust in you.