Can you try introducing him to a harness and lead? Maybe start with just five minutes a day and work up to more over time?
Has he been neutered yet? Intact males have an urge to go out and find territory and females that is nearly impossible to squelch.
Another possibility, if you have a fenced backyard, is to do modifications to the fence to keep him from climbing it. If you don't have a fenced back yard, would it be possible to make a "catio"? I saw one on Facebook that was made from an Ikea shelving unit and chickwire that didn't look too expensive to create.
Our big male cat loves to explore the grass verge between the back fence of our townhouse complex and a busy road. It makes my hair stand up on end and I keep a firm hand on the leash while he does it. There is no way I'd let him roam by himself, besides the two busy roads nearby, there have been coyotes sighted in the area.