OK, several days have passed with no responses, so I'll give away the answer:
The National Cycle League.
It was a short-lived attempt at creating cycling as a city-based league.
It was a half-baked attempt administered by a largely incompetent NFL cast-off commissioner and several misguided owners.
I came across the Miami Wave t-shirt while cleaning out a closet. I had hoped that some readers of this board would have stories/insight.
Maybe it's best to bury it in the backyard.