Injection of Lower Hybrid Heating and Current Drive (LHCD) into the current ramp-up phase of JET discharges can produce extremely reversed q-profiles characterized by a core region of near zero current density (within Motional Stark Effect diagnostic measurement errors). Non-inductive, off-axis co-current drive induces a back electromotive force inside the non-inductive current radius that drives a negative current in the plasma core. The core current density does not go negative, although current diffusion calculations indicate that there is sufficient LHCD to cause this. The clamping of the core current density near zero is consistent with n = 0 reconnection events redistributing the core current soon after it goes negative. This is seen in reduced MHD simulations and in nonlinear resistive MHD simulations which predict that these discharges undergo n = 0 reconnection events that clamp the core current near zero.