J.,
Boys especially have night time wetting issues long after we as parents think it should be over. My own two boys did ok, but my younger brother had multiple issues even into his teens. I was nearly out of high school when he was going through all this, so I have many memories of the issue. Pull ups didn't exist then, we used waterproof mattress covers and extra sheets folded up on his bed every night. We tried no liquid after 6 pm, we tried alarm clocks set to go off in the middle of the night, we tried those battery operated alarms that cliped to his underware and went off when it got wet.
Bottom line was this: He is a crazy deep sleeper and his bladder didn't grow as fast as the rest of his body. That made for wet beds night after night. We never punished him for it, it wasn't in his control.
I did a lot of research on the topic when I became the mother of boys. In a nutshell, take away the pull ups, put a plastic mattress cover on the bed and some kind of absorbent pad under him at night. Keep doing what you're doing with limited liquids, that's always a smart idea. He will outgrow it one of two ways. His bladder will catch up with the rest of his body or he will not like being wet during the night and will learn to wake up and use the bathroom if he needs to.
My oldest son did have an issue with wetting at the age of six after he'd had a major medical issues and had been hospitalized for a couple of weeks. He lost his bladder control for a while and was back in diapers for a short time. It took about a month and a half before he was able to control night time wetting issues again, but it took me just taking the pull ups away before he made the switch back to being dry.
Good luck, don't stress and worry about. They do grow out of it eventually.