Years ago when my sister-equivalent had iggies the little one was deaf as well. One day after ballet class I was sitting on the couch and Sharkey crawled into my lap, stuck her head in my leotard and then maneuvered her entire body in there (yes, I let her because I wanted to see what the silly girl was trying to do) stuck her head out and went promptly to sleep. For the next 8 or 9 nine years of her life, she crawled inside people's tops/sweaters, etc. It was soothing to her. Do you think that Little Dude would sleep, or at least relax if you let him do this (assuming you want to do it)? It is actually quite easy to deal with as they are so small. You just have to remember to sling an arm under your new "belly" when you get up!
We have a lot of pictures of several of us with our little alien baby in our tops. Some with head out, some without so it looks really alien.