For example, the man eats greedily, gradually, with no hesitation
As commonly understood, "gradually" and "greedily" suggest completely opposite paces. "Greedily" implies quickly, or with an urgency to complete the task. It just doesn't go with "gradually", it causes cognitive dissonance.
The sentence is an awful use of the English language. However, one adverb does not contradict the other. One verb refers to speed whilst the other refers to volume (excess).
"Gradually, the politicians greedily increased their pay and benefits."
- That's not great either.