Less forward-looking variables than good eigenvalues

Yes, usually there is something fundamentally wrong, typically the timing of some predetermined variables like the (capital) stock. There is one and only one correct timing dictated by economic intuition. You cannot simply shift some variables by one period.

In your case, it might for example have to do with the split between

exp(N) = exp(Ne)+exp(Nn);
see [Timing of capital in two sector economy)