Advice on getting external interview oppurtunities

I have been in Amazon for a long time now and I have been trying to move out. However I am not getting any opportunities to interview. I did have two. I did not get an offer from a late stage startup and the other i got an offer that was not attractive enough to move. I am an L8 in Amazon and while i have a network outside Amazon, i have not been able to use my network to really get a shot at interviews. Clearly I am missing something. How do i get more opportunities to interview as an executive, should i work with a headhunter? I am now making an effort to just not wait but get help from any avenues including Blind. Any insights from senior level folks in Blind on how can i market that i am looking and get calls for interviews? Thanks