Building a network through cold emailing...

As someone who has 15 years of corporate finance experience as a business unit CFO trying to break into private equity and trying to cold email/LinkedIn message people, I'd love this forum's help in answering the following questions:

1) Who should I be targeting? Managing Partners seem too high on the food chain to care. Associates seem too powerless to actually matter. Is VP/Directors the sweet spot? Or am I better off targeting recruiters only?

2) How would you recommend structuring the message as someone who has 15 years of corporate finance experience as a business unit CFO but no IB experience? Should that detail even go into the message?

3) If I get no response, is it worth following up? Don't want to pester but at the same time I get it, people are busy and are likely to ignore the first message.

4) Which firms should I target? The Blackstones of the world probably have more opportunities but I feel the smaller MM or LMM firms will probably be more responsive?

As always, thanks in advance for the help.