We're solving these exact problems by developing Mighty Spring (https://www.mightyspring.com).

LinkedIn has always been a good professional networking tool. But because it's a professional networking tool, exploring new opportunities is rife with risk (as the OP alludes to). Great opportunity discovery is about what you want to do, not just what you have done, and that isn't necessarily public information.

Mighty Spring helps you find interesting jobs discretely -- a private place for you to manage your career.

ps. We're in private beta, but will expedite invites to all you hacker news folks that sign up :)