Normally going out to snack would have been my go to option. It just so happened that last night we were all eating supper up at church. He had already finished and refused to sit down for a drink or more food. The whole thing of getting mad, to cheating, to tantruming all progressed in less than 2 minutes.
I'm really interested in the way you described your dd needing sensory input. That may be my ds. I've noticed he is not normal or average in that area. Example: at the playground when other kids just play normally, my ds will climb up to the top just to jump off and land in a roll through the rocks. I guess I had never connected those behaviors to having anything to do with meltdowns.
I may also reevaluate his bedtime. Last year, he didn't handle kindergarten well at all and had to be in bed by 5:30 to avoid meltdowns. We slowly pushed bedtime back to 7:00 over the summer (still seems early) but that may be part of the problem. I had hoped he could handle a later bedtime with homeschool and rest time during the day.
We have seen a therapist. He can only do so much when the behaviors are almost always at home and not seen by others. He did encourage us that ds will hopefully be able to function nearly at age level by 9 or 10.