The "white out" effect you're talking about appears much worse in photos than it does in real life. In person, unless you are stretching the lycra to its absolute breaking point, you'll still have fairly decent color saturation.
Honestly, unless you're looking to invest huge sums of time and money into the research and development needed to print on multiple colors of lycra (Also, good luck finding a shop who will do it for you...I've called probably 3 dozen shops in the past and only one said they would try it, then when I went to place an order told me they were no longer willing to try it) just stick with printing it on white fabric. If you've never seen one of these bad boys in person, you'll just have to take my word on it that it's really not as bad as it seems in the pictures.
And darkening the colors will help a little up to a point, but beyond that won't help much because it's not that you're mixing colors like you would with paint, it's that white is being revealed as the fabric stretches. And whether you have a lighter color or a darker color on the fabric, it's still going to show the same amount of white when stretched.
Good luck.
-Nick