Dualman7, hows it going man? Tell us your plans on getting past this idiosyncrasy of yours. Your post here is a good start but you got keep going!
Schwan, being nonchalant only works if you know you'll see the girl again. Otherwise it's "oh, that guy seems intresting...oh well" *keep walking*. A missed opportunity!
Here is my modification on your theme.
As I spot the girl I look away as if I am looking at achitecture or something
. Then at mid distance I take a good look at her and make eye contact. If I like her I'll keep eye contact, and if she doesn't turn away I say "HI"
The intresting thing about looking away is that it gives girls an oportunity to take a good look at you without feeling threatened by eye contact. Most girls simply stare forward and avoid eye contact because they don't wan't creeps thinking they are intrested just because the girl checked them out.
also,
looking away eyes down: good thing, say "hi"
looking away sideways: bad thing
looking away eyes up: you made a fool of yourself - say something funny!