My 3 (this week) year old entire male rott has pee'd in the house the last 2 mornings and I am not impressed

It has been marking rather than emptying his bladder and yesterday it was in my bedroom up the curtains and on the carpet and today up the cloakroom door.
He doesn't tend to get upstairs unless he is well supervised and yesterday he came up while I was in the shower so wasn't supervised. Today I was getting ready for work and he did it up the cloakroom door while I wasn't there. I don't want to go back to crating him at every moment I can't supervise him but also can't watch him every waking moment.
He is entire as he is a total wuss but fear aggressive. Both my trainer and my vet advised against neutering as he needs the testosterone to give him the levels of confidence he does have. Neutered rotts also have a significantly increased risk of bone cancer in comparison with entire so I would only neuter as a very last resort so please no suggestions that neutering will fix this.
As far as I am aware there are no in-season bitches around. He hasn't been paying particular attention to any of the neighbours houses while we have been out and hasn't wanted to be outdoors more than usual so I am fairly sure it is not an in-season bitch causing this.
Any tips on how to stop this is or even suggestions why it may be occurring? If this is him at maturity trying to assert his authority he is in for a shock! I have never caught him in the act and he has been fully clean since being a puppy. When puberty was kicking in (8/9 months) he did mark in the house twice, once on my other dogs bed and the other time on my bedroom carpet (different place to now and it has been washed countless times by the carpet shampoo man since then).
All suggestions and input welcome