How to search for a Career Counselor / Specialist for Life Sciences?
You're focusing on finding a career counselor. Most career counselors I've known are general purpose, trying to help people with the basics of cover letter and resume construction, the typical flow of the hiring process, etc. Never heard of one specializing in the life sciences or, for that matter, any sciences, but I suppose that might have changed over the years.
A recruiter is not a career counselor. A recruiter is a matchmaker. There are lots of recruiters for the IT fields, but don't imagine for a moment they play the role of career counselors for computer science grads. If a recruiter is telling you to leave off the PhD aspect of your training, he or she is doing it for practical reasons. Crappy and  unfair and humbling? Yep.
Nearly everyone I know professionally, at the higher levels outside of academia, got his or her job because of his or her network and knew how to present him or herself appropriately at interviews. It's a thing you learn.
Cattle calls through web sites?  They're not always what they seem. But you're playing the numbers.
One thing you don't speak of is what other career avenues you've explored outside of the life sciences. Widen the playing field,  develop your network. We write our own life stories, but sometimes need ideas on how to start. Rather than a career counselor, step back to assess the situation. A cognitive therapist can help there.