The mechanism for the reaction of atomic chlorine with vibrationally excited methane is investigated by measurement of correlated state and scattering distributions using the method of core extraction (see preceding paper). Laser photolysis of molecular chlorine creates monoenergetic chlorine atoms (>98% (ClP3/2)-P-2) that react with vibrationally excited methane molecules prepared by linearly polarized infrared laser excitation. The resulting HCl product population distributions are determined by (2+1) resonance-enhanced multiphoton ionization (REMPI), and the differential cross section for each product rovibrational state is measured by core extraction. Approximately 30% of the product is formed in HCl(upsilon=1,J) with a cold rotational distribution; the remaining population is formed in HCl(upsilon=0,J) and is more rotationally excited. We observe a rich variation of the scattered flux that is dependent on the internal-energy state of the product. The HCl(upsilon=1) product is sharply forward scattered for low J and becomes nearly equally forward-backward scattered for high J; the HCl(upsilon=0,J) product is back and side scattered. The reactions of Cl with C-H stretch-excited methane (CH4) and C-H stretch-excited CHD3 are found to have similar angular and internal-state distributions. Observation of the spatial anisotropy of the HCl(upsilon=0,J=3) product shows that significant vibrational excitation of the methyl fragment does not occur. The measured spatial anisotropy is most consistent with a model in which backscattered HCl(upsilon=0,J=3) is formed in coincidence with slight methyl vibrational excitation and the forward-scattered HCl(upsilon=0,J=3) is formed in coincidence with no methyl excitation. The approach of the attacking chlorine atom with respect to the C-H stretch direction can be varied by rotating the plane of polarization of the infrared excitation. A marked steric effect is observed in which Cl atoms approaching perpendicular to the C-H stretch preferentially yield forward-scattered HCl(upsilon=1) product. On the other hand, the reaction is weakly dependent on the rotational quantum state of CH4(upsilon(3)=1,J), and on the rotational polarization. The data are consistent with a model that has a widely open "cone of acceptance" in which the impact parameter controls the internal-state and scattering distributions of the HCl product.