Honestly, multi-channel outreach is the only thing that's been working for me lately too. I start on LinkedIn - just a quick view of their profile, maybe a thoughtful comment on something they've posted. Then a couple of days later, I'll send a very short video message, either on LinkedIn or via email. Nothing polished - just me, talking directly to them about something I noticed about their business.
Plain email on its own? Maybe three or four replies out of a hundred. Adding a personal video bumps that to around one in five for me. I've given up leading with pain points - it feels pushy. Instead, I latch onto something timely - a new hire, a funding round, a product launch - and connect it to a specific result we've delivered for someone similar. Keep the video under a minute, the email to about three lines.
It usually takes four to six touches spread over a couple of weeks before anyone bites. The trick is to give them something new each time - not just "checking in". That just annoys people.
What kind of service are you selling, and do you have a client success story you can lean on without sounding salesy?