Hey Ross,
I've tried similar eye contact experiments before. I found that making eye contact is easier if you start looking at them when the two of you are about 30 feet (10 meters) apart. When do you start looking at them? Do you wait too long?
Also, smile before your eyes meet. It shows that you're happy with yourself, and makes you look friendly and easy to approach. Don't worry about looking weird. Everyone looks weird from time to time. I know most people don't smile, but most people don't want to meet new strangers.
Remember, if you do what do the same things you've always done, you'll just get the same results.