I think you've done a good thing by making videos which can be shown to the movements disorder doctor. People with Spasmodic Dysphonia do not benefit from DBS so most of us know little about it. I happen to be aware of DBS because I get the DMRF magazine.
Before you venture down the DBS path, you need to get an absolutely certain diagnosis which can be validated by at least two unrelated medical specialists. Further, you should find out if there have been any cases of DBS performed on a child you son's age.
What is very scary to me is to hear you say that doctors are leaning towards DBS but do not have a full and complete diagnosis of what is wrong with him. they are talking about brain surgery and don't know for certain what it wrong with him. This should cause you to slow down and proceed with the utmost caution.