This paper presents two accurate continuous-discrete extended Kalman filters designed for estimating stiff continuous-time stochastic models in chemical engineering. These methods are grounded in the Gauss-type nested implicit Runge-Kutta formulas of orders 4 and 6, which are applied for treating moment differential equations (MDEs). The local and global error controls implemented in these filters ensure that the MDEs are integrated with negligible errors, numerically. The latter raises the accuracy of state estimation and makes our state estimators more effective than the traditional extended Kalman filter based on the Euler-Maruyama discretization of order 0.5 and the continuous-discrete cubature Kalman filter grounded in the Ito-Taylor approximation of order 1.5. The variable-stepsize fashion of these new filtering techniques allows also for the accurate state estimation of chemical stochastic models with infrequent measurements. The designed state estimators are examined numerically on the stochastic Oregonator model, which is a famous stiff example in chemistry research.