Small number of customer outreach question

I wonder about the best methods to reach out to a small pool of people.

Let's say, I really want to talk to 100 people in Private Equity. Yes, they are on Linkedin. Yes, I can find their emails. But cold outreach probably wont take me very far (and it hasnt) - with average reply rates at 5% I get maybe 2 convos out of it and then I am out of people to email.

So, what is the right way to do this? I keep running into this problem of having very specific and (well) defined pools of people but it means that the n seems way to small for cold email.

Maybe more generally: how should I approach thinking of channels in general?