The slow translational dynamics of glassy isotropic fluids of hard polyatomic rods and spherocylinders of aspect ratios up to forty have been theoretically investigated. The approach is based on a preaveraging of orientational degrees of freedom to a center-of-mass description, and a nonlinear stochastic Langevin equation of motion that includes activated barrier hopping on a nonequilibrium free energy profile. Variable site bond length effects have also been studied for symmetric diatomics and linear triatomics. The excluded volume driven ideal glass transition (GT) boundary is predicted to be a nonmonotonic function of particle length-to-width ratio, and rather remarkably resembles the random close packing volume fraction of nonspherical granular objects. The location of the rod and spherocylinder ideal GT boundary relative to the percolation threshold, isotropic-nematic liquid crystal phase transition, and mechanical jamming volume fraction has been determined. The ideal GT signals a crossover to noise-driven activated barrier hopping dynamics. The consequences of shape anisotropy on the entropic barrier height, localization length, elastic modulus, yield stress and nongaussian dynamic heterogeneity aspects have been studied. The theory has also been applied to suspensions of rigid disks, in both the isotropic and discotic liquid crystalline state, and the results contrasted with the rod-like systems.