There isn't a solution to that. You have to talk to other points, and you have to do so from a connection you are on. That information, on ANY network in the world, is inevitable.
The only thing you can do is obscure it as much as possible so that people can't tell WHAT you did over the connection, or WHAT you passed to those others. They will be able to know who they were, but unless you can introduce sufficient plausible deniability (with Tor, that's just by using random people as the next hop), you can't do anything about that.
I don't think that's a problem we should waste time trying to solve. You aren't going to be able to obscure your endpoint's knowledge when 100% of the time someone is paying money for that endpoint to be connected to other endpoints. We do not have a darknet.
But it's also not that big a deal. With proper encryption and enough fake / routing data running through your connection with that encryption (and PFS), it's meaningless. All that can happen is someone can say "you were online, and so was John". If that's enough to convict you, you have bigger problems than the protocol of the network you used.