Need Advice Debugging MLE Code to Estimate an ARMA(p,q)
If anyone per chance runs into the same issue,

The reason the MLE is exploding is that a system with explosive roots (eigenvalues outside the unit circle), might make the Kalman-filter predictions explode at a point, and thus creating a few very large MLE values. 

The solution is to rig the MLE function s.t. if any of the eigenvalues lie outside the unit circle, return an MLE >=0. Thus the optimization algorithm will be forced to find a stationary local minimum.