Aren't the terms 'going within,' 'contacting one's inner self' and the like much too general?
Depends on where they lead one. As they say in the real estate world, it's all about location. Many favor comfort areas within their ego-mind as the places where going within takes them. What eventually follows are more contradictions and confusion.
You're saying they're kidding themselves about their spiritual aspirations?
No, sincerity may be there, but it's easy to forget that it isn't the ego-mind that ever awakens.
Then going within means going outside of ego-mind.
It means going beyond the confines of ego-mind's mazes, connecting with a spacious presence that is everywhere. You could say that within our total makeup, not just the ego-mind, are doorways to that spacious presence that contains all that is, within which this world is but a dot.