I coach a lot of CEO's, but they weren't CEO's when I started coaching them. As they got better at what they did, more opportunities opened up for them.
The same is true in your business network. The people you start getting to know now will become more influential over time which will open up more opportunities for you and them.
It sounds like you want to skip a step, in other words, by connecting with influential people you'll instantly gain a Trusted Advisor Community. It's just that it doesn't really work that way. You have to get to know people step by step. And the first step is to surround yourself with people you like and trust. Get to know them and help them and over time you will develop your own network, which is much more valuable (to you and them) than piggybacking on someone else's network.
In terms of how I connect with people, I'm always happy to talk to someone who wants to get to know me better. I'm leery if it seems that they just want access to my network or just want to sell me something.
My specific advice is to join groups on LinkedIn that have similar minded people to you, get involved in the conversation, and get to know them. Over time you'll build up a strong network which I think is what you're looking for anyway.
If you want to talk in more detail about techniques for meeting more people and expanding your referral network feel free to set up a call.