We have developed an approach called QED-CASCI to provide ground-and excited-state polaritonic surfaces with a balanced description of strong correlation effects among electronic and photonic degrees of freedom. This method can provide a platform for ai-CQED when both strong electron correlation and strong light-matter coupling are important and can be leveraged to obtain multiple polaritonic potential energy surfaces and couplings that can be leveraged for ab initio molecular dynamics simulations of polariton chemistry. We have implemented two different formulations of QED-CASCI: PN-QED-CASCI which is formulated in the photon-number basis and CS-QED-CASCI which is formulated in the coherent state basis. Both methods were applied to a range of model systems for which we can also provide a numerically exact benchmark using QED-FCI. We have shown that both methods converge to numerically identical answers in the limit that the photon basis becomes complete, but that CS-QED-CASCI shows accelerated convergence that becomes particularly prominent for polar and charged species. The efficiency of our serial implementation was demonstrated on the naphthalene molecule in a (12,12) active space where we can solve for multiple polaritonic states with the inclusion of 100 photonic basis states in roughly 4 hours on a single CPU.