We present a detailed analysis of nonempirically tuned range-separated functionals, with both short- and long-range exchange, for calculating the static linear polarizability and second hyperpolarizabilities of various polydiacetylene (PDA) and polybutatriene (PBT) oligomers. Contrary to previous work on these systems, we find that the inclusion of some amount of short-range exchange does improve the accuracy of the computed polarizabilities and second hyperpolarizabilities. Most importantly, in contrast to prior studies on these oligomers, we find that the lowest-energy electronic states for PBT are not closed-shell singlets, and enhanced accuracy with range-separated DFT can be obtained by allowing the system to relax to a lower-energy broken-symmetry solution. Both the computed polarizabilities and second hyperpolarizabilities for PBT are significantly improved with these broken-symmetry solutions when compared to previously published and current benchmarks. In addition to these new analyses, we provide new large-scale CCSD(T) and explicitly correlated CCSD(T)-F12 benchmarks for the PDA and PBT systems, which comprise the most complete and accurate calculations of linear polarizabilities and second hyperpolarizabilities on these systems to date. These new CCSD(T) and CCSD(T)-F12 benchmarks confirm our DFT results and emphasize the importance of broken-symmetry effects when calculating polarizabilities and hyperpolarizabilties of π-conjugated chains.