Fully-aromatic, thermotropic, liquid crystalline random copolyesters of 4-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid (HNA) were studied at elevated temperatures with H-1 NMR. Proton T-1 measurements provide high-frequency characterization of the glass transition. Proton rotating frame relaxation time (T-1 rho) measurements near room temperature are sensitive to HBA rotational motions; these motions are expected when there is monomer length-scale chain conformational disorder. In melt-quenched samples, this disorder is spatially homogeneous (i.e., the material solidifies without crystallization). Annealing below the nominal solidification temperature (T-s) results only in a slight, uniform lessening of this disorder. For samples annealed above T-s, proton T-1 rho measurements show a spatially distinct component in which monomeric rotational motions are suppressed. Spin-diffusion experiments indicate this component has a mean thickness of 10 +/- 2 nm. H-1-C-13 (cross polarization-magic-angle spinning) CP-MAS measurements indicate that these ordered regions are enriched in HBA. The fraction and HNA content of the "cocrystallites" decrease at higher annealing temperatures. We discuss a new conceptual model of solid ordering in highly sequence-frustrated, stiff HBA/HNA copolyesters that is consistent with these and previously reported data.