IMHO. You can be stubborn (like me) and suffer through countless adjustment and dangerous test runs and MAYBE find a combination that stops the head shake. Or...
You can be smart (like me)
I bought a fork mounting bracket and a VW beetle dampner for $100 delivered. (eBay) Bolt to the sidcar. Few minutes and or hours.
IT ABSOLUTELY, POSITIVELY, INSTANTLY transformed my hack
I wrote about it here.
Fact is, no one else on this board had the unique bike, sidecar, tire, weight, rider, road combination I had. But My head was shaking violently and that's what dampners are for. It flat works for me.