It is well known that laser pulses can break electronic structure symmetry of atoms and molecules, specifically by superposing two (or more) states with different irreducible representations (IRREPs). Recently, our theory group together with the experimental group of Professor Kenji Ohmori, our partner at the Institute for Molecular Science in Okazaki, have shown that laser pulses can also achieve the reverse process, symmetry restoration. For this purpose, the pulse for symmetry restoration was designed as a copy of the pulse for symmetry breaking, with attosecond precision of the proper time delay. Here we develop the theory for new scenarios coherent molecular symmetry breaking and restoration. The extensions are from previous applications of weak circularly polarized ultrafast (fs) laser pulses with Gaussian shapes to intense linearly polarized ultrafast laser pulses that do not need to be transform-limited, e.g. they may have down- and up-chirps. As a proof-of-principle, quantum dynamics simulations demonstrate restoration of D6h symmetry of the aligned model benzene molecule, after laser induced D6h→C2v symmetry breaking. The success depends on two criteria: (i) the laser pulse that restores symmetry is designed as a time-reversed copy of the pulse that breaks symmetry; and (ii) their time delay must be chosen with attosecond precision such that the wavefunction at the central time between the pulses is a superposition of two states with different IRREPs but with the same or with opposite phases (modulo 2π).