Why can't you have radical neck dissection on both sides ?
I was diagnosed Stage 4 left tonsil cancer with multiple lymph node invilvement (left side), I was also poorly differentiated SCC. I remebered my ENT surgeon said if I had nodes on both sides, he would do the neck dissection on botrh sides.
You could have neck diseection on the sides with large lymph nodes then let the Chemo/RAD take care of the rest. In my opinion, get rid of the tumor is important