We present Floquet theory-based predictions and electrically detected magnetic resonance (EDMR) experiments scrutinizing the nature of two-photon magnetic resonance shifts of charge-carrier spin states in the perdeuterated π-conjugated polymer poly[2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylene vinylene] (d-MEH-PPV) under strong magnetic resonant drive conditions (radiation amplitude B1 ~ Zeeman field B0). Numerical calculations show that the two-photon resonance shift with power is nearly drive-helicity independent. This is in contrast to the one-photon Bloch-Siegert shift that only occurs under non-circularly polarized strong drive conditions. We therefore treated the Floquet Hamiltonian analytically under arbitrary amplitudes of the co- and counter-rotating components of the radiation field to gain insight into the nature of the helicity dependence of multi-photon resonance shifts. In addition, we tested Floquet-theory predictions experimentally by comparing one-photon and two-photon charge-carrier spin resonance shifts observed through room-temperature EDMR experiments on d-MEH-PPV-based bipolar injection devices [i.e., organic light emitting diode structures (OLEDs)]. We found that under the experimental conditions of strong, linearly polarized drive, our observations consistently agree with theory, irrespective of the magnitude of B1, and therefore underscore the robustness of Floquet theory in predicting nonlinear magnetic resonance behaviors.