First, I wanna say this definitely hit home for me. Can empathize with your son (I was a longtime bedwetter) and you as a parent of a bedwetter. Before I get all emotional, I will tell you from my Early Childhood studies, "normal" boys may take up to age 7-8 to master night time toilet training, girls 6-7.
In extreme cases, like myself, bedwetting runs in my fam... my grandpa, my dad, my bro, me. All of us were in our teens before we had dry nights. And now my daughter, who is 7, wets the bed. Fortunately we live in an age of Pull Ups so we don't have to shatter her self esteem over wet sheets. If he's comfortable with Pull Ups, I wouldn't bother trying to "make" him stop. You can't.
All you can do is limit fluid intake 1-2 hours before bedtime and make him use the toilet. If he wants to "fix" his problem, he'll let you know. Until then, treat it as any other developmental milestone. Wait patiently until your pediatrician expresses concern. Remember bedwetting is not a sign of weakness, laziness, or lack of intelligence and you can't teach people's bodies when to tinkle or to sleep less soundly. Every body is develops at its own pace.
Please, I had well-intentioned mother who tried to cure me... used rewards, punishment, threats of telling my friends, not allowing me to attend sleepovers, etc. I'm begging you to give him some time. Stress, like worrying over disappointing you, only aggrevates things and will make him more aware of how different he is.
Side bar: My daughter's been in charge of her Pull Ups since she was 5yrs old. I keep them in her PJs drawer and flushable wipes and mini trash bags in her undies drawer. It's prepared her for sleepovers. She can put them on and properly dispose of them with little to no adult help. Also makes less work for Mommy :)