I've gotten good at playing an aggressive Lucio. Like scary good.
Enemies never expect the support to rush them and run circles around them. This is exactly what I do. I've killed many bastions by myself speed boosting around them and the amp always messes them up. Hanzos have rage quit because they can't hit a moving target that easily. It's hilarious watching 2-3 enemies chasing down a Lucio they can't catch while my team takes the objective.
Of course, I still heal plenty, and even speed boost my team often to the see effect. Its hilarious.
Lucio is a really good aggresive support, maybe that's why it's my favorite character in the game.
I agree spinning and shooting around unalerted opponents is great, specially when you use speed boost and amp it up.