Good Morning K.!
Ohhh... I can so feel your pain! My (now) 10 year old was a consistant bed wetter til he was 8. (I am making an assumption that when you say "consistant", that this is not a new issue due to the new blended family.) I bet my son and I had a lot of the feelings and frustrations you and your son have about it now!
My son was an EXTREMELY heavy sleeper. To wake him up after the first hour of sleep was like trying to rouse the dead!! And even after you got him sitting up with his eyes open for a while... he still would not remember being got up in the morning. So I guess it was no surprise that he couldn't get himself up to go to the bathroom at night.
What worked for him was to follow a behavior plan for 3-6 months. We purchased a bed wetting alarm for $70. (We got the Wet Stop alarm from www.wet-stop.com I see they have come down in price and are now $50.) There is a sensor that attaches to their underwear and then there is an alarm that attaches to their PJ's up near their shoulder. When the sensor gets wet even a drop.. the alarm goes off. When we first started the plan, he would have an accident (we would hear the alarm, HE wouldn't even move!!) we would get him up, take him to the bathroom, have him change his PJ's, have him help change the sheets, take the wet ones to the washing machine.. then before he went back to bed we would give him a code word to remember in the morning. We would tell it to him and have him write it down 5 times. (And do you know that for about 3 weeks... after doing all those things.. he still could not remember the word in the morning??? His brain was that deep in sleep!!)
He also would sleep through the alarm on the loudest setting that was right near his ear!!
Then gradually he began remembering the code word in the morning (we had a different one every night), and he started being able to wake up himself when the alarm went off. And after about 6 months.. we were able to stop using the alarm, and he has been dry ever since... no accidents!!
I wish I could tell you there is a quick fix for this problem, but unless it is a medical condition (which I think you have ruled out) you are left with 2 choices..committing to a long term behavior plan (which takes away from our beauty sleep!!) or waiting for him to out grow it.
While you are going through the trainning it can be very tiring and frustrating... but the results (for us!!) have been worth it! We have saved oodles in pull ups (the alarm is DEFINATELY worth the investment, and I am not having to wash sheets,blankets, PJs, and underwear all the time. And my son isn't afraid and embarressed to go on vacation, or stay the night at a friend or family members.. or have them stay here.
This may not be the answer you wanted to hear... but it is the truth in our situation!! This technique is the same as the ones you hear people paying thousands of dollars to help their kids. You are mostly paying for the professionals to help walk you through the steps. If that's helpful.. maybe consider making the investment. If you're a person that can stay disciplined and on top of a project.. I'd save the money and do it myself. But you know best what will help most in your family!!
I wish you and your son the best of luck in whatever you decide is best!
Have a great day!
Peace,
B.
P.S. If you're a Christian... don't forget to pray about it :-)