Apologies I do not have enough reputation points to post this as a comment. You might have already considered other electronic structure methods, but I would like to suggest consider using density matrix renormalisation group (DMRG) based methods for the calculations. DMRG is highly suitable for modelling conjugated polymers. For example, here is an example of DMRG-CASSCF calculations on linear polyenes, and here is an example of calculations on acenes.
DMRG methods are supported by several open source quantum chemistry packages, and I found psi4, which utilises CheMPS2 particularly easy to use.
As pointed out by @wzkchem5, DMRG does not take into account dynamical correlations. For NEVPT2/DMRG calculations on polyene systems, please see this and this.