We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at the level of singles and doubles excitations. Our results show that already with the cc-pVTZ basis, the transcorrelated distinguishable cluster method gets close to the complete basis limit and near full configuration interaction quality values for relative energies of over thirty atoms and molecules. To gauge the performance in different correlation regimes, we also investigate the breaking of the nitrogen molecule with transcorrelated coupled cluster methods. Numerical evidence is presented to further justify an efficient way to incorporate the major effects coming from the three-body integrals without explicitly introducing them into the amplitude equations.