Are there herbal treatments that thin the blood the way aspirin does?

Yes. Sludgy blood - find out why it is that way? It usually is a diet in excess of fat, cholesterol, refined sugar so if you figure out the problem you can prevent this. My favorite is deltanol - delta tocopherol.
Aspirin. I don't know about herbal but high dose fish oil is thought to thin the blood although it has not been tested for this property in research. Aspirin certain has the research behind it in terms of thinning the blood.