Ari, you're giving all of us a chance to remind ourselves about perfectionistic thinking!
You're going to make yourself miserable (and freak yourself out) if you set up the false choice of: you're either "totally independent" of people or "totally dependent" on people.
When you write about not being able to do "any" of the things on the out of sight out of mind list because people will think you are too needy I think you might be seeing relationships in a black and white way. You get this in part from our culture. We grow up thinking (for some reason that I can't fathom) that if we grow up "correctly" we'll eventually "grow out of" interdependent relationships. As if when we are "truly mature" we won't need anyone. I think that's silly- and counter to our nature as social creatures. This cultural view helps promote black and white thinking about relationships- and it makes a lot of us feel as if we are somehow failing if we want, need and/or have interdependent relationships. Relationships change of course. For example, someone's relationships with his parents will not be exactly the same when he is 5, 10, 23 or 47, right? But they can always be there for each other, be intertwined in each other's lives, be supportive and helpful.
But, back to what you were writing about, Ari. If you depend on someone it does not mean you are "needy." We all get to and need to depend on people throughout our lives. That's normal. In fact, one of the terrific things about close relationships is the particular way we get to, and can, depend on someone, and they can depend on us. It's a mutual thing- an interdependence- where everybody benefits.
Anyone in your life who really cares about you will jump at the chance to help you with this out of sight out of mind thing, or any other thing. Another neat thing about close relationships is the mutual assistance and mutual giving that goes on between people; it's a great joy for everyone involved. It's fun both to give and to receive from someone you love. (I'm aware that people who have eating disorders struggle with the idea of receiving- they find it so much easier to give, and receiving makes them feel too vulnerable- things worth working on, since close relationships where we can really give AND receive are the most rewarding).