We report angular dependent 77Se NMR measurements on the partially quenched, metallic, and magnetic field-induced spin density wave (FISDW) states of (TMTSF)2CIO4. To correlate the NMR data with the FISDW phase diagram, electrical transport was also measured concurrently in some cases. Similar measurements on (TMTSF)2PF6 allow comparison of the behavior of the NMR signal of the spin density wave (SDW) transition with that of the FISDW transition. We present details of the experimental findings including the enhancement behavior, and correlations of the angular dependence of the NMR spectra with the spin-lattice relaxation rate 1/T1. A possible model to describe the behavior of the NMR signal intensity and 1/T1 in terms of a Hebel-Slichter mechanism upon crossing the metal-FISDW transition is presented.