Although the addition of "got" may not follow the strictest syntax rules I believe it's use can be justified here because it serves as an intensifier that emphasizes the need to act is greater than the use of "have" alone connotes.
Also, when the contraction "I've" is used then the addition of "got" improves the word structure sonically by preserving the normal rhythm of a sentence because the contraction works as a single word that serves as the noun, or rather, pronoun of the sentence and leaves a need for another verb.