Poor thing! It's hard enough developing into a "tween" without this trouble, too!
My son had trouble, too, but it tapered off around age 10 and we haven't had trouble since thank goodness.
The best thing that we did, was NOT make it an issue. The idea was to try to not let it effect his self-confidence.
The only thing he had to do, was to remove his sheets for me, so i knew when to wash them and I made his bed for him, so it wasn't a constant "chore" as a punishment in his eyes. We never "spoke" about it.
I just want you to know that i agree with your decision to avoid any meds to help control this. I believe it will take care of itself.....in time. The hard part is waiting for it to be over.
I'm not sure if you know, but they do have "boxers" for older boys to wear at night, to help absorb while they sleep. I don't know much about them, but I know of another mom who claimed they worked great for them.
Just keep trying to to not make it embarrassing for him. Try not to loose your temper when changing his sheets AGAIN, because he might interpret that as anger towards him (I had trouble with that). I believe that it is normal, and it will eventually "run it's course".
Hang in there :O)
~N.