The meltdowns my daughter had when she woke in the middle of the night were very different from those during the day. In the morning, she didn't even remember them. I believe she had trouble coming out of deep sleep and we saw the same behavior you describe. It appeared she was totally awake, but all she did was scream and wouldn't respond to questions coherently. The average person sleeps in 90 minute cycles, so you might want to try changing the wet diaper at a time he isn't in deep sleep, then doing whatever sooths him to get him back to sleep. I learned in a book about SPD (can't remember which one) that most kids with sensory issues can't stand having their back rubbed in the upward direction or in circles, but they prefer firm downward strokes on the back. I have found this to be true with my daughter to calm her and get her back to sleep.
For daytime tantrums I implemented some techniques in the book Effective Parenting for the Hard to Manage Child. This helped a little, but I later discovered she was reacting to BHT (a preservative). I put her on the Feingold Diet and haven't seen a meltdown in a long time. She still has occasional tantrums, but they are the usual ones you see with all kids and are very short lived.